Decomposition of degenerate Gromov-Witten invariants
Algebraic Geometry
2020-06-04 v4
Abstract
We prove a decomposition formula of logarithmic Gromov-Witten invariants in a degeneration setting. A one-parameter log smooth family X->B with singular fibre over b_0 \in B yields a family M(X/B,\beta) -> B of moduli stacks of stable logarithmic maps. We give a virtual decomposition of the fibre of this family over b_0 in terms of rigid tropical curves. This generalizes one aspect of known results in the case that the fibre X_{b_0} is a normal crossings union of two divisors. We exhibit our formulas in explicit examples.
Keywords
Cite
@article{arxiv.1709.09864,
title = {Decomposition of degenerate Gromov-Witten invariants},
author = {Dan Abramovich and Qile Chen and Mark Gross and Bernd Siebert},
journal= {arXiv preprint arXiv:1709.09864},
year = {2020}
}
Comments
63 pages, major revision of v2: streamlined exposition with the core results rewritten with simplified and cleaner proofs (now in {\S}2.4-2.6 and {\S}3). To appear in Compositio Math. Accepted version