Punctured logarithmic maps
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866929518703280128 |
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| 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 |