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89  Extracted references

This appendix imports the per-paper literature-summary notes verbatim from the project knowledge base. Each entry preserves the note’s original “Used here for” and “Project relevance” lines and its abstract as written; only the citation key has been remapped to its canonical build key where the note’s filename key was stale (the remap is stated in each entry). The Papers Index navigation note is not imported.

89.1 ABE22 — Valery Alexeev, Adrian Brunyate, Philip Engel (2022): Compactifications of moduli of elliptic K3 surfaces

Bibkey: ABE22 (imported from note AB21; remapped AB21 to ABE22). Cited as (Alexeev et al. 2022).

Abstract. KSBA and toroidal compactifications for elliptic K3 surfaces, used in the paper as background for stable-pair compactification techniques.

  • Used here for: background on stable-pair compactifications of K3 moduli, especially in the IAS / stable-limits context.

  • Project relevance: supplies KSBA techniques and comparison principles for compactifications of K3 moduli spaces.

89.2 AEGS25 — Valery Alexeev, Philip Engel, D. Zack Garza, Luca Schaffler (2023): Compact Moduli of Enriques Surfaces with a Numerical Polarization of Degree 2

Bibkey: AEGS25 (imported from note AEGS23; remapped AEGS23 to AEGS25). Cited as (Alexeev et al. 2025).

Abstract. We describe a geometric, stable pair compactification of the moduli space of Enriques surfaces with a numerical polarization of degree 2, and identify it with a semitoroidal compactification of the period space.

Contents of the note (the paper’s table of contents):

    1. Introduction — 1
    1. General setup — 3
    1. Cusps and Coxeter diagrams — 8
    1. Dlt models via integral-affine structures on the disk and \(\mathbb{RP}^2\) — 16
    1. Toroidal, semitoroidal, and KSBA compactifications — 28
    1. ABCDE surfaces — 31
    1. KSBA stable degenerations of Enriques surfaces — 38
  • References — 41

89.3 AET23 — Valery Alexeev, Philip Engel, Alan Thompson (2023): Stable pair compactification of moduli of K3 surfaces of degree 2

Bibkey: AET23 (unchanged). Cited as (Alexeev et al. 2023).

Abstract. Stable-pair compactification for degree-2 K3 surfaces, providing a direct KSBA model for a key K3 moduli problem adjacent to the Coble and Enriques constructions.

  • Used here for: the stable-pair side of degree-2 K3 compactifications in the stable-limits discussion.

  • Project relevance: forms part of the KSBA background for comparing period-domain compactifications with geometric compactifications.

89.4 AN06 — Valery Alexeev, Viacheslav V. Nikulin (2006): Del Pezzo and K3 surfaces

Bibkey: AN06 (unchanged; not listed in the citation-key audit — used as-is). Cited as (Alexeev and Nikulin 2006).

Abstract. Reference on del Pezzo and K3 surfaces used for Coxeter diagrams, reflective lattices, and parabolic subdiagram calculations.

  • Used here for: the Coble Coxeter diagrams and the identification of maximal parabolic subdiagrams.

  • Project relevance: supports the cusp-diagram computations around \((9,9,1)_1\) and the \(\wB_7(2)\) parabolic.

89.5 AS15 — Michela Artebani, Alessandra Sarti (2015): Symmetries of order four on K3 surfaces

Bibkey: AS15 (unchanged; not remapped in the audit — used as-is. Note: the audit records that at one citation site — the Rational Sextic Hurwitz/Lemma 2.2 attribution — the key AS15 was wrong and was corrected to AD18; that correction concerns the site, not this Artebani–Sarti note, whose key is retained). Cited as (Artebani and Sarti 2015).

Abstract. Study of order-4 nonsymplectic symmetries on K3 surfaces, used here for the branched-cover and Hurwitz-type calculations behind the classical Coble sextic construction.

  • Used here for: the Hurwitz-type calculation that identifies the proper transform of the rational sextic with the anti-bicanonical divisor in the classical Coble construction.

  • Project relevance: supplies one of the cited inputs behind the sextic-to-Coble transition.

89.6 BHO+12 — Blekherman, Hauenstein, Ottem, Ranestad, Sturmfels (2012): Algebraic boundaries of Hilbert’s SOS cones

Bibkey: BHO+12 (imported from note BHO+11; remapped BHO+11 to BHO+12 per the audit’s year-drift resolution, arXiv 2011 to Compositio Math. 148 (2012), Zotero GJZ44LJI. Note: the original note frontmatter carried only the placeholder title “BHO+11”; the author/title/year shown here are supplied from the audit’s resolution of the work. The audit is internally inconsistent about this work — the “RESOLVED” block pins it to BHO+12, while a later verification line states it is “not in Zotero, still unresolved”; the resolved key is used here). Cited as (Blekherman et al. 2012).

Abstract. Appendix reference for the Severi variety \(V_{6,10}\) of rational plane sextics with ten nodes.

  • Used here for: the statement that the nodal rational sextics relevant to the classical Coble construction form a Severi variety \(V_{6,10}\) whose generic point has ten \(A_1\)-singularities.

  • Project relevance: supports the appendix note separating the generic ten-node Coble sextic from more degenerate rational sextics.

89.7 CD12 — Serge Cantat, Igor Dolgachev (2012): Rational surfaces with a large group of automorphisms

Bibkey: CD12 (unchanged; audit confirms CD12 = Cantat–Dolgachev, live Zotero PMC33V8M). Cited as (Cantat and Dolgachev 2012).

Abstract. Reference on rational surfaces with large automorphism groups, including Cremona-special point sets, Coble and Halphen surfaces, and moduli consequences.

  • Used here for: Cremona-special and unnodal Coble surfaces, the Halphen blowdown lemma, and the modular-curve description of Enriques and Coble cusps.

  • Project relevance: provides geometric structure theorems for rational Coble surfaces and their automorphism groups.

89.8 CDL25 — Francois Cossec, Igor Dolgachev, Christian Liedtke (2024): Enriques surfaces I

Bibkey: CDL25 (imported from note CDL24; remapped CDL24 to CDL25). Cited as (Cossec et al. 2025).

Abstract. Draft reference on Enriques and Coble surfaces used throughout the paper for 2-elementary lattice tables, fixed loci, and Coble/Halphen geometry.

  • Used here for: the lattice table for Coble surfaces, fixed-locus formulas for the K3 cover involution, boundary-component geometry, and Halphen/Coble results.

  • Project relevance: this is the main modern reference behind many Coble facts imported into the paper’s introduction and appendix.

89.9 Cob19 — Arthur B. Coble (1919): The ten nodes of the rational sextic and of the Cayley symmetroid

Bibkey: Cob19 (unchanged). Cited as (Coble 1919).

Abstract. Classical source for the rational sextic with ten nodes and the associated Coble surface construction.

  • Used here for: the original plane-sextic construction of the classical Coble surface.

  • Project relevance: foundational citation for the blowup of the ten nodes of a rational sextic.

89.10 Cob29 — Arthur B. Coble (1929): Algebraic geometry and theta functions

Bibkey: Cob29 (unchanged). Cited as (Coble 1929).

Abstract. Classical monograph on point configurations, Cremona geometry, and the background of Coble surfaces.

  • Used here for: classical background on point configurations and the historical geometry surrounding Coble surfaces.

  • Project relevance: complements the original sextic-node construction with the broader classical theory.

89.11 DK25 — Igor Dolgachev, Shigeyuki Kondo (2024): Enriques surfaces II

Bibkey: DK25 (imported from note DK24; remapped DK24 to DK25). Cited as (Dolgachev and Kondō 2025).

Abstract. Draft reference used for terminal Coble surfaces of K3 type, K3 double covers, basic rational surface structure, and Halphen constructions.

  • Used here for: the double-cover construction \(X \to S\), the structure of terminal Coble surfaces of K3 type, and the Halphen-surface description.

  • Project relevance: one of the main sources for the paper’s introductory and geometric facts about Coble surfaces.

89.12 DM20 — Igor Dolgachev, Dimitri Markushevich (2020): Lagrangian tens of planes, Enriques surfaces and holomorphic symplectic fourfolds

Bibkey: DM20 (imported from note DM19; remapped DM19 to DM20). Cited as (Dolgachev and Markushevich 2020).

Abstract. Source used for the definition of Coble surfaces and related Enriques-surface geometry.

  • Used here for: an explicit modern definition of Coble surfaces.

  • Project relevance: supplies a concise reference point for the paper’s opening definition of the Coble locus.

89.13 Dol12 — Igor V. Dolgachev (2012): Classical algebraic geometry

Bibkey: Dol12 (unchanged; the audit remaps a specific site from Dol12 to Dol17 but does not retire the Dol12 key, which is this note’s Classical Algebraic Geometry reference). Cited as (Dolgachev 2012).

Abstract. Modern reference on classical algebraic geometry, used here for the geometric degeneration picture of Coble surfaces and the quartic del Pezzo model coming from isotropic sequences.

  • Used here for: the geometric description of Coble surfaces as degenerations of Enriques/K3 quotients and the linear systems \(|2f_i+2f_j|\) mapping to quartic del Pezzo surfaces.

  • Project relevance: anchors the source citations for the geometric Coble remarks migrated into the vault.

89.14 Dol17 — Igor Dolgachev (2017): Salem numbers and Enriques surfaces

Bibkey: Dol17 (unchanged). Cited as (Dolgachev 2017).

Abstract. Background source on Enriques-surface automorphisms and lattice-theoretic constructions.

  • Used here for: the geometric remark on degenerating an Enriques K3 cover to the Coble case.

  • Project relevance: provides background on Enriques involutions and automorphisms that informs the geometric discussion.

89.15 DZ99 — Igor Dolgachev, D. Zhang (1999): Coble rational surfaces

Bibkey: DZ99 (unchanged). Cited as (Dolgachev and Zhang 1999).

Abstract. Foundational paper on Coble rational surfaces, including their relationship to Halphen surfaces and degenerations of Enriques surfaces.

  • Used here for: the relation between Coble surfaces and Halphen surfaces, and for the broader geometry of Coble rational surfaces.

  • Project relevance: one of the main classical-modern references for the geometry behind the paper’s moduli problem.

89.16 GK20 — Rational plane sextics with worse singularities (appendix reference)

Bibkey: GK20 (unchanged; not listed in the citation-key audit — used as-is. Note: the original note frontmatter carried only the placeholder title “GK20” with no author or year, so no fuller title is supplied here). Cited as (Golla and Kütle 2020).

Abstract. Appendix reference for rational plane sextics with worse singularities, used to note that rational sextics need not lie in the ten-node Severi stratum.

  • Used here for: the example that rational sextics can have fewer than ten \(A_1\)-points when more degenerate singularities such as \(A_2\) occur.

  • Project relevance: supports the caveat that the classical Coble construction uses a special generic nodal stratum rather than all rational sextics.

89.17 Hor77 — Eiji Horikawa (1978): On the periods of Enriques surfaces. II

Bibkey: Hor77 (imported from note Hor78; remapped Hor78 to Hor77, the global key for “Periods II”). Cited as (Horikawa 1977).

Abstract. Classical period-domain source behind the Horikawa model for Enriques and Coble surfaces.

  • Used here for: the \(\mathbf{P}^1 \times \mathbf{P}^1\) model with a \(\tau\)-invariant anti-bicanonical branch curve.

  • Project relevance: underlies the Horikawa construction that realizes the Coble locus as a boundary of Enriques moduli.

89.18 KK72 — Peter Kiernan, Shoshichi Kobayashi (1972): Satake compactification and extension of holomorphic mappings

Bibkey: KK72 (unchanged). Cited as (Kiernan and Kobayashi 1972).

Abstract. Technical compactification result used to extend locally closed period-domain embeddings to Baily-Borel compactifications.

  • Used here for: extending the lattice-induced embeddings on period spaces to morphisms of Baily-Borel compactifications.

  • Project relevance: supplies the compactification-theoretic justification for the maps between \(F_{\Co}\), \(F_{\mathrm{En}}\), and \(\fttz\).

89.19 Mor81 — David R. Morrison (1981): Semistable degenerations of Enriques’ and hyperelliptic surfaces

Bibkey: Mor81 (unchanged). Cited as (Morrison 1981).

Abstract. Original source for flower, stalk, pot, and flowerpot degenerations of Enriques-type surfaces.

  • Used here for: the flowerpot description of degenerations expected to model parts of the Coble boundary.

  • Project relevance: historical source behind the degeneration picture later reformulated in dlt / KSBA language.

89.20 Nik80 — V. V. Nikulin (1979): Integer symmetric bilinear forms and some of their geometric applications

Bibkey: Nik80 (imported from note Nik79; remapped Nik79 to Nik80, the global key for the Integer Symmetric Bilinear Forms paper). Cited as (Nikulin 1980).

Abstract. Fundamental reference for 2-elementary lattices, discriminant forms, primitive embeddings, and orthogonal-group surjectivity.

  • Used here for: classification of 2-elementary lattices, uniqueness of primitive embeddings, and surjectivity statements for orthogonal groups.

  • Project relevance: this is the lattice-theoretic backbone of the Coble, Enriques, and degree-2 K3 embedding arguments.

89.21 Nue15 — Howard Nuer (2016): Unirationality of moduli spaces of special cubic fourfolds and K3 surfaces

Bibkey: Nue15 (unchanged; the audit maps Nue16 to Nue15 as the single global entry). Cited as (Nuer 2015).

Abstract. Reference used for the statement that the nodal quotient appearing on the Enriques boundary is a Coble surface.

  • Used here for: the identification of a quotient with a Coble surface in the Enriques-boundary construction.

  • Project relevance: provides a supporting citation for the geometric transition from nodal K3 covers to Coble surfaces.

89.22 Ols04 — Martin C. Olsson (2004): Semistable degenerations and period spaces for polarized K3 surfaces

Bibkey: Ols04 (unchanged). Cited as (Olsson 2004).

Abstract. Foundational treatment of semistable degenerations and period spaces for polarized K3 surfaces, used here for flowerpot degenerations and their relation to Coble boundary behavior.

  • Used here for: the flower, stalk, and pot terminology and the Type I / flowerpot degeneration picture applied to Coble surfaces.

  • Project relevance: provides the older degeneration language that the vault uses to relate the Coble boundary to modern KSBA and IAS viewpoints.

89.23 PS71 — I. I. Pjateckii-Shapiro, I. R. Shafarevich (1971): A Torelli theorem for algebraic surfaces of type K3

Bibkey: PS71 (unchanged). Cited as (Piatetski-Shapiro and Shafarevich 1971).

Abstract. Classical Torelli theorem for algebraic K3 surfaces, used to pass from lattice data to period-domain moduli.

  • Used here for: the Torelli input behind the direct period-domain construction of \(F_{\Co}\).

  • Project relevance: justifies reconstructing the Coble K3 cover from Hodge-theoretic lattice data.

89.24 Sha81a — Jayant Shah (1981): Projective degenerations of Enriques’ surfaces

Bibkey: Sha81a (imported from note Sha81; remapped Sha81 to Sha81a, distinguishing Shah’s Enriques paper from the global Sha81). Cited as (Shah 1981).

Abstract. Projective-degeneration source for Enriques surfaces, cited alongside Morrison in the discussion of flowerpot degenerations.

  • Used here for: projective degenerations related to the flowerpot picture.

  • Project relevance: forms part of the classical degeneration background that the paper interprets on the Coble boundary.

89.25 Ste91 — Hans Sterk (1991): Sterk 1991 note

Bibkey: Ste91 (imported from note Ste91-note; remapped the note’s Ste91-note filename key to the work’s citation key Ste91, which the audit confirms exists in the global bib). Cited as (Sterk 1991).

Abstract. Supplemental note linking the existing Ste91 extraction to its role in the Coble paper.

  • Used here for: divisibilities of isotropic vectors, cusp labels, and the identification of Sterk cusp 2.

  • Project relevance: the Coble cusp map to \((18,0,0)_1\) is interpreted through Sterk’s cusp classification.