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Log BPS numbers of log Calabi-Yau surfaces
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Choi, Jinwon, van Garrel, Michel, Katz, Sheldon and Takahashi, Nobuyoshi (2020) Log BPS numbers of log Calabi-Yau surfaces. Transactions of the American Mathematical Society . doi:10.1090/tran/8234 ISSN 0002-9947.
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WRAP-Log-BPS-numbers-log-Calabi-Yau-surfaces-2020.pdf - Accepted Version - Requires a PDF viewer. Download (1103Kb) | Preview |
Official URL: https://doi.org/10.1090/tran/8234
Abstract
Let $ (S,E)$ be a log Calabi-Yau surface pair with $ E$ a smooth divisor. We define new conjecturally integer-valued counts of $ \mathbb{A}^1$-curves in $ (S,E)$. These log BPS numbers are derived from genus 0 log Gromov-Witten invariants of maximal tangency along $ E$ via a formula analogous to the multiple cover formula for disk counts. A conjectural relationship to genus 0 local BPS numbers is described and verified for del Pezzo surfaces and curve classes of arithmetic genus up to 2. We state a number of conjectures and provide computational evidence.
Item Type: | Journal Article | |||||||||||||||||||||
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Subjects: | Q Science > QA Mathematics | |||||||||||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||||||||||||||
Library of Congress Subject Headings (LCSH): | Calabi-Yau manifolds, Gromov-Witten invariants | |||||||||||||||||||||
Journal or Publication Title: | Transactions of the American Mathematical Society | |||||||||||||||||||||
Publisher: | American Mathematical Society | |||||||||||||||||||||
ISSN: | 0002-9947 | |||||||||||||||||||||
Official Date: | 3 November 2020 | |||||||||||||||||||||
Dates: |
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DOI: | 10.1090/tran/8234 | |||||||||||||||||||||
Status: | Peer Reviewed | |||||||||||||||||||||
Publication Status: | Published | |||||||||||||||||||||
Reuse Statement (publisher, data, author rights): | “First published in Transactions of the American Mathematical Society in [volume/issue number and year], published by the American Mathematical Society,” and the copyright notice in proper form must be placed on all copies. | |||||||||||||||||||||
Access rights to Published version: | Restricted or Subscription Access | |||||||||||||||||||||
Copyright Holders: | © 2020 American Mathematical Society | |||||||||||||||||||||
Date of first compliant deposit: | 2 July 2020 | |||||||||||||||||||||
Date of first compliant Open Access: | 3 July 2020 | |||||||||||||||||||||
RIOXX Funder/Project Grant: |
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