Year: 2017
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Tehrani, Mohammad Farajzadeh
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3043634505