TY - JOUR
T1 - Moduli of fibered surface pairs from twisted stable maps
AU - Ascher, Kenneth
AU - Bejleri, Dori
N1 - Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2019/6/1
Y1 - 2019/6/1
N2 - 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.
AB - 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.
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U2 - 10.1007/s00208-018-1697-5
DO - 10.1007/s00208-018-1697-5
M3 - Article
AN - SCOPUS:85047413758
SN - 0025-5831
VL - 374
SP - 1007
EP - 1032
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 1-2
ER -