Four-dimensional Fano quiver flag zero loci

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Title: Four-dimensional Fano quiver flag zero loci
Authors: Kalashnikov, E
Item 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.
Issue Date: 15-May-2019
Date of Acceptance: 23-Apr-2019
URI: http://hdl.handle.net/10044/1/73854
DOI: https://dx.doi.org/10.6084/m9.figshare.c.4491959
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.
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Commission of the European Communities
Funder's Grant Number: EP/N03189X/1
682603
Keywords: 01 Mathematical Sciences
02 Physical Sciences
09 Engineering
Publication Status: Published
Open Access location: https://doi.org/10.1098/rspa.2018.0791
Online Publication Date: 2019-05-15
Appears in Collections:Pure Mathematics
Mathematics



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