Punctured logarithmic maps

Fuente: arXiv
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Main Authors: Abramovich, Dan, Chen, Qile, Gross, Mark, Siebert, Bernd
Format: Preprint
Published: 2020
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_version_ 1866929518703280128
author Abramovich, Dan
Chen, Qile
Gross, Mark
Siebert, Bernd
author_facet Abramovich, Dan
Chen, Qile
Gross, Mark
Siebert, Bernd
contents We introduce a variant of stable logarithmic maps, which we call punctured logarithmic maps. They allow an extension of logarithmic Gromov-Witten theory in which marked points have a negative order of tangency with boundary divisors. As a main application we develop a gluing formalism which reconstructs stable logarithmic maps and their virtual cycles without expansions of the target, with tropical geometry providing the underlying combinatorics. Punctured Gromov-Witten invariants also play a pivotal role in the intrinsic construction of mirror partners by the last two authors in arXiv:1909.07649, conjecturally relating to symplectic cohomology, and in the logarithmic gauged linear sigma model in upcoming work of the second author with Felix Janda and Yongbin Ruan.
format Preprint
id arxiv_https___arxiv_org_abs_2009_07720
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle Punctured logarithmic maps
Abramovich, Dan
Chen, Qile
Gross, Mark
Siebert, Bernd
Algebraic Geometry
14N35 (14D23)
We introduce a variant of stable logarithmic maps, which we call punctured logarithmic maps. They allow an extension of logarithmic Gromov-Witten theory in which marked points have a negative order of tangency with boundary divisors. As a main application we develop a gluing formalism which reconstructs stable logarithmic maps and their virtual cycles without expansions of the target, with tropical geometry providing the underlying combinatorics. Punctured Gromov-Witten invariants also play a pivotal role in the intrinsic construction of mirror partners by the last two authors in arXiv:1909.07649, conjecturally relating to symplectic cohomology, and in the logarithmic gauged linear sigma model in upcoming work of the second author with Felix Janda and Yongbin Ruan.
title Punctured logarithmic maps
topic Algebraic Geometry
14N35 (14D23)
url https://arxiv.org/abs/2009.07720