Moduli of fibered surface pairs from twisted stable maps

Kenneth Ascher, Dori Bejleri

Research output: Contribution to journalArticle

Abstract

In this paper, we use the theory of twisted stable maps to construct compactifications of the moduli space of pairs (X→ C, S+ F) where X→ C is a fibered surface, S is a sum of sections, F is a sum of marked fibers, and (X, S+ F) is a stable pair in the sense of the minimal model program. This generalizes the work of Abramovich–Vistoli, who compactified the moduli space of fibered surfaces with no marked fibers. Furthermore, we compare our compactification to Alexeev’s space of stable maps and the KSBA compactification. As an application, we describe the boundary of a compactification of the moduli space of elliptic surfaces.

Original languageEnglish (US)
Pages (from-to)1007-1032
Number of pages26
JournalMathematische Annalen
Volume374
Issue number1-2
DOIs
StatePublished - Jun 1 2019
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Moduli of fibered surface pairs from twisted stable maps'. Together they form a unique fingerprint.

  • Cite this