Four-dimensional Fano quiver flag zero loci
File(s)
Published version
OA Location
Author(s)
Kalashnikov, Elana
Type
Journal Article
Abstract
Quiver flag zero loci are subvarieties of quiver flag varieties cut out by sections of representation theoretic vector bundles. We prove the Abelian/non-Abelian correspondence in this context: this allows us to compute genus zero Gromov–Witten invariants of quiver flag zero loci. We determine the ample cone of a quiver flag variety, and disprove a conjecture of Craw. In the appendices (which can be found in the electronic supplementary material), which are joint work with Tom Coates and Alexander Kasprzyk, we use these results to find four-dimensional Fano manifolds that occur as quiver flag zero loci in ambient spaces of dimension up to 8, and compute their quantum periods. In this way, we find at least 141 new four-dimensional Fano manifolds.
Date Issued
2019-05-15
Date Acceptance
2019-04-23
Citation
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2019, 475 (2225), pp.1-23
ISSN
1364-5021
Publisher
The Royal Society
Start Page
1
End Page
23
Journal / Book Title
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume
475
Issue
2225
Copyright Statement
© 2019 The Authors. Published by the Royal Society under the terms of the
Creative Commons Attribution License http://creativecommons.org/licenses/
by/4.0/, which permits unrestricted use, provided the original author and
source are credited.
Creative Commons Attribution License http://creativecommons.org/licenses/
by/4.0/, which permits unrestricted use, provided the original author and
source are credited.
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Commission of the European Communities
Identifier
https://royalsocietypublishing.org/doi/10.1098/rspa.2018.0791
Grant Number
EP/N03189X/1
682603
Subjects
01 Mathematical Sciences
02 Physical Sciences
09 Engineering
Publication Status
Published
Date Publish Online
2019-05-15