Logarithmic Quasimaps

Mohammed Shafi

doi:10.1016/j.aim.2023.109469

Logarithmic Quasimaps

Mohammed Shafi^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

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Abstract

We construct a proper moduli space which is a Deligne–Mumford stack parametrising quasimaps relative to a simple normal crossings divisor in any genus using logarithmic geometry. We show this moduli space admits a virtual fundamental class of the expected dimension leading to numerical invariants which agree with the theory of Battistella–Nabijou where the latter is defined.

Original language	English
Article number	109469
Number of pages	30
Journal	Advances in Mathematics
Volume	438
Early online date	9 Jan 2024
DOIs	https://doi.org/10.1016/j.aim.2023.109469
Publication status	Published - Feb 2024

Bibliographical note

Acknowledgments
I would like to wholeheartedly thank Dhruv Ranganathan for suggestions and guidance with this project as well as for invaluable feedback on drafts. I owe a great deal of thanks to Navid Nabijou for many helpful discussions as well as for feedback. I would also like to thank Tom Coates and Rachel Webb for helpful conversations. This work was supported by the EPSRC Centre for Doctoral Training in Geometry and Number Theory at the Interface, grant number EP/L015234/1 and the UKRI Future Leaders Fellowship through grant number MR/T01783X/1.

Keywords

Logarithmic quasimaps
Logarithmic Gromov-Witten theory

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10.1016/j.aim.2023.109469Licence: Creative Commons: Attribution (CC BY)

ShafiQ2024LogarithmicFinal published version, 571 KBLicence: Creative Commons: Attribution (CC BY)

https://www.sciencedirect.com/science/article/pii/S0001870823006126Licence: Creative Commons: Attribution (CC BY)

Open Mirror Geometry for Landau-Ginzburg Models
Kelly, T.
Medical Research Council
1/11/20 → 30/06/25
Project: Research Councils

Cite this

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AB - We construct a proper moduli space which is a Deligne–Mumford stack parametrising quasimaps relative to a simple normal crossings divisor in any genus using logarithmic geometry. We show this moduli space admits a virtual fundamental class of the expected dimension leading to numerical invariants which agree with the theory of Battistella–Nabijou where the latter is defined.

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Logarithmic Quasimaps

Abstract

Bibliographical note

Keywords

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Open Mirror Geometry for Landau-Ginzburg Models

Cite this