Moduli of fibered surface pairs from twisted stable maps
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Author(s)
Ascher, Kenneth
Bejleri, Dori
Date Issued
May 26, 2018
Publisher
Springer Berlin Heidelberg
Version
Author's final manuscript
Abstract
Abstract
In this paper, we use the theory of twisted stable maps to construct compactifications of the moduli space of pairs
$$(X \rightarrow C, S + F)$$
(
X
→
C
,
S
+
F
)
where
$$X \rightarrow C$$
X
→
C
is a fibered surface, S is a sum of sections, F is a sum of marked fibers, and
$$(X,S+F)$$
(
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1007/s00208-018-1697-5
