Moduli of surfaces with an anti-canonical cycle

Abstract

We prove a global Torelli theorem for pairs (Y,D), where Y is a smooth projective rational surface and D is an effective anti-canonical divisor which is a cycle of rational curves. This Torelli theorem was conjectured by Friedman in 1984. In addition, we construct natural universal families for such pairs.

Final version. Much simplified proofs. To appear in Compositio

References in corpus (2)

• Mirror symmetry for log Calabi-Yau surfaces I
• On the ample cone of a rational surface with an anticanonical cycle

Cited by in corpus (27)

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• Smoothings and Rational Double Point Adjacencies for Cusp Singularities
• Classification of Rank 2 Cluster Varieties
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• Symplectic log Calabi-Yau surface---deformation class
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