Moduli of surfaces with an anti-canonical cycle. (9th October 2014)

• Record Type: Journal Article
• Authors: Gross, Mark; Hacking, Paul; Keel, Sean
• Is Part Of: Compositio mathematica. Volume 151:Number 2(2015:Mar.)
• Page Start: 265
• Page End: 291
• Publication Date: 2014-10-09
• Subjects: 14J26, -- 14J10 (primary); Looijenga pairs, -- rational surfaces, -- moduli; Mathematics -- Periodicals; 510
• DOI: 10.1112/S0010437X14007611
• Languages: English
• ISSNs: 0010-437X

Abstract

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