Loughborough University
Browse

Geometry of canonical genus 4 curves

Download (556.82 kB)
journal contribution
posted on 2024-01-24, 16:42 authored by Fatemeh Rezaee

We apply the machinery of Bridgeland stability conditions on derived categories of coherent sheaves to describe the geometry of classical moduli spaces associated with canonical genus 4 space curves via an effective control over its wall‐crossing. This article provides the first description of a moduli space of Pandharipande–Thomas stable pairs that is used as an intermediate step toward the description of the associated Hilbert scheme, which in turn is the first example where the components of a classical moduli space were completely determined via wall‐crossing. We give a full list of irreducible components of the space of stable pairs, along with a birational description of each component, and a partial list for the Hilbert scheme. There are several long standing open problems regarding classical sheaf theoretic moduli spaces, and the present work will shed light on further studies of such moduli spaces such as Hilbert schemes of curves and moduli of stable pairs that are very hard to tackle without the wall‐crossing techniques.

Funding

PCDS (University of Edinburgh)

Birational Models of Singular Fano 3-folds

Engineering and Physical Sciences Research Council

Find out more...

Wall-crossing: from classical algebraic geometry to differential geometry, mirror symmetry and derived algebraic Geometry

UK Research and Innovation

Find out more...

RC Starting Grant WallXBirGeom: 337039

RCConsolidatorGrantWallCrossAG: 819864

NSF: DMS-144014

History

School

  • Science

Published in

Proceedings of the London Mathematical Society

Volume

128

Issue

1

Publisher

Wiley

Version

  • VoR (Version of Record)

Rights holder

© The Author

Publisher statement

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Acceptance date

2023-10-23

Publication date

2024-01-01

Copyright date

2023

Notes

The author was supported by the EPSRC Grant EP/T015896/1 at Loughborough University whilst completing this paper.

ISSN

0024-6115

eISSN

1460-244X

Language

  • en

Depositor

Fatemeh Rezaee; Deposit date: 17 January 2024

Article number

e12577

Usage metrics

    Loughborough Publications

    Licence

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC