Journal article
Limits of stable maps in a semi-stable degeneration
Geometriae dedicata, Vol.216(6), 66
09/12/2022
DOI: 10.1007/s10711-022-00731-5
Abstract
Given a semistable degeneration with a simple normal crossings central fiber, Abramovich et al. (Compositio Mathematica 156(10):2020–2075, 2020) proved a degeneration (or decomposition) 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 derive a (conjectural) degeneration formula similar to ACGS’s formula, and work out an explicit example. The results are expected to hold in the symplectic category as outlined in an earlier version (Farajzadeh-Tehrani in Towards a degeneration formula for the Gromov–Witten invariants of symplectic manifolds.
arXiv:1710.00599v1
[math]) of this paper.
Details
- Title: Subtitle
- Limits of stable maps in a semi-stable degeneration
- Creators
- Mohammad Farajzadeh-Tehrani - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Geometriae dedicata, Vol.216(6), 66
- Publisher
- Springer Netherlands
- DOI
- 10.1007/s10711-022-00731-5
- ISSN
- 0046-5755
- eISSN
- 1572-9168
- Grant note
- DMS-2003340 / Directorate for Mathematical and Physical Sciences (http://dx.doi.org/10.13039/100000086)
- Language
- English
- Date published
- 09/12/2022
- Academic Unit
- Mathematics
- Record Identifier
- 9984296001702771
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