Moduli of surfaces with an anti-canonical cycle

2012/11/30 by Mark Gross, Paul Hacking, Seán Keel +1 · 3 citations
Computer Science · Mathematics · #Algebra over a field #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Divisor (algebraic geometry) #Mathematics #Moduli #Moduli space #Polynomial and algebraic computation #Pure mathematics #math.AG #msc:14J10 #msc:14J26

paper · pdf · doi:10.1112/s0010437x14007611

published as Compositio Math. 151 (2015) 265-291 · Final version. Much simplified proofs. To appear in Compositio

arxiv created 2014/06/30 · openalex publication_date 2014/10/09 · arxiv updated 2019/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Abstract We prove a global Torelli theorem for pairs (Y,D) where Y is a smooth projective rational surface and D∈ |-K_Y| is a cycle of rational curves, as conjectured by Friedman in 1984. In addition, we construct natural universal families for such pairs.

Citations

• Introduction to Toric Varieties. (AM-131)
• Mirror symmetry for log Calabi-Yau surfaces I

Cited by

• Splitting symplectic monodromy
• Constructing Fano 3-folds from cluster varieties of rank 2
• Tropical theta functions and log Calabi–Yau surfaces