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Punctured logarithmic maps

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arxiv 2009.07720 v3 pith:KZQOIEET submitted 2020-09-16 math.AG

Dan Abramovich , Qile Chen , Mark Gross , Bernd Siebert This is my paper · ORCID
classification math.AG
keywords logarithmicmapspuncturedgromov-wittenstableallowapplicationarxiv
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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.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Mirrors to toric degenerations via intrinsic mirror symmetry

    math.AG 2026-08 conditional novelty 8.0 of 10

    For special toric degenerations of K3 surfaces, the intrinsic mirror and the universal toric degeneration mirror coincide after restricting to the minimal relative Gross-Siebert locus and basechanging by the polarization.

  2. The many faces of a logarithmic scheme

    math.AG 2024-12 conditional novelty 8.0 of 10

    Every coherent logarithmic scheme decomposes into a jointly surjective collection of fine logarithmic faces, computable by monoidal Gröbner basis algorithms.

  3. Gromov-Witten theory with maximal contacts

    math.AG 2019-08 conditional novelty 8.0 of 10

    For simple normal crossings divisors, logarithmic and local/naive Gromov-Witten invariants with maximal contacts differ, and this paper gives the first counterexamples plus a blowup formula measuring the difference.

  4. Quantum periods, toric degenerations and intrinsic mirror symmetry

    math.AG 2025-01 conditional novelty 7.0 of 10

    The classical periods of the intrinsic mirror algebra of a log Calabi-Yau Fano pair reproduce the regularized quantum periods of the Fano variety.

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