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

20 Downloads (Pure)

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

Access to Document

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 → 31/10/24
Project: Research Councils

Cite this

@article{d5b5253eabfa4b668688f0983c49e039,

title = "Logarithmic Quasimaps",

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.",

keywords = "Logarithmic quasimaps, Logarithmic Gromov-Witten theory",

author = "Mohammed Shafi",

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.",

year = "2024",

month = feb,

doi = "10.1016/j.aim.2023.109469",

language = "English",

volume = "438",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Elsevier",

}

TY - JOUR

T1 - Logarithmic Quasimaps

AU - Shafi, Mohammed

N1 - 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.

PY - 2024/2

Y1 - 2024/2

N2 - 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.

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.

KW - Logarithmic quasimaps

KW - Logarithmic Gromov-Witten theory

U2 - 10.1016/j.aim.2023.109469

DO - 10.1016/j.aim.2023.109469

M3 - Article

SN - 0001-8708

VL - 438

JO - Advances in Mathematics

JF - Advances in Mathematics

M1 - 109469

ER -

Logarithmic Quasimaps

Abstract

Bibliographical note

Keywords

Access to Document

Fingerprint

Projects

Open Mirror Geometry for Landau-Ginzburg Models

Cite this