Moduli of fibered surface pairs from twisted stable maps
Moduli of fibered surface pairs from twisted stable maps
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来自扭曲稳定图的纤维表面对的模量
DOI：
10.1007/s00208-018-1697-5
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发表时间：
2016
影响因子：
1.4
通讯作者：
Dori Bejleri
中科院分区：
文献类型：
--
作者：
Kenneth Ascher;Dori Bejleri
In this paper, we use the theory of twisted stable maps to construct compactifications of the moduli space of pairs (X→C,S+F)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(X \rightarrow C, S + F)$$\end{document} where X→C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X \rightarrow C$$\end{document} is a fibered surface, S is a sum of sections, F is a sum of marked fibers, and (X,S+F)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(X,S+F)$$\end{document} 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.
In this paper, we use the theory of twisted stable maps to construct compactifications of the moduli space of pairs (X→C,S+F)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(X \rightarrow C, S + F)$$\end{document} where X→C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X \rightarrow C$$\end{document} is a fibered surface, S is a sum of sections, F is a sum of marked fibers, and (X,S+F)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(X,S+F)$$\end{document} 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.
DOI：
10.1016/j.aim.2017.08.035
发表时间：
2016-10
期刊：
arXiv: Algebraic Geometry
影响因子：
--
作者：
Kenneth Ascher;Dori Bejleri
通讯作者：
Kenneth Ascher;Dori Bejleri
影响因子：
1.8
作者：
Kenneth Ascher;Dori Bejleri
通讯作者：
Kenneth Ascher;Dori Bejleri