半稳定退化中稳定映射的极限
Limits of stable maps in a semi-stable degeneration
摘要：
给定一个具有简单正规交叉中心纤维的半稳定退化，Abramovich-Chen-Gross-Siebert [3]证明了一个退化公式，它将光滑纤维中稳定映射的模空间与中心纤维中对数光滑映射的某些模空间联系起来.在本文中，我们从分析的角度研究同一问题。我们证明了中心纤维中的极限稳定映射满足特定的组合和分析条件。进一步，我们解释了由这些条件所引起的模空间的变形-阻塞理论，导出了退化公式，并给出了一个显式例子。本文的早期版本[8]包含了辛范畴的这些思想的概要。
英文摘要：
Given a semistable degeneration with a simple normal crossings central fiber, Abramovich-Chen-Gross-Siebert [3] proved a degeneration formula that relates the moduli spaces of stable maps in smooth fibers to certain moduli spaces of log-smooth maps in the central fiber. In this paper, we study the same problem from an analytic point of view. We prove that the limiting stable maps in the central fiber satisfy specific combinatorial and analytical conditions. Furthermore, we explain the deformation-obstruction theory of the moduli spaces arising from these conditions, derive a degeneration formula, and work out an explicit example. The earlier version [8] of this paper contains an outline of these ideas for the symplectic category.
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