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Four-dimensional Fano quiver flag zero loci
1Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2AZ, UK.
Proceedings. Mathematical, Physical, and Engineering Sciences
|June 26, 2019
Summary
This study introduces quiver flag zero loci, enabling computation of Gromov-Witten invariants. It also identifies 141 new four-dimensional Fano manifolds, advancing algebraic geometry research.
Area of Science:
- Algebraic Geometry
- Representation Theory
- Mathematical Physics
Background:
- Quiver flag varieties are fundamental objects in algebraic geometry.
- Representation theory provides tools to study these varieties.
- Gromov-Witten invariants are crucial in enumerative geometry and string theory.
Purpose of the Study:
- To compute genus zero Gromov-Witten invariants of quiver flag zero loci.
- To determine the ample cone of quiver flag varieties.
- To discover new four-dimensional Fano manifolds.
Main Methods:
- Utilizing the Abelian/non-Abelian correspondence.
- Analyzing sections of representation theoretic vector bundles.
- Investigating quiver flag zero loci as subvarieties.
Main Results:
- Successfully computed genus zero Gromov-Witten invariants for quiver flag zero loci.
- Determined the ample cone of quiver flag varieties.
- Disproved a conjecture by Craw.
- Identified at least 141 new four-dimensional Fano manifolds.
Conclusions:
- The Abelian/non-Abelian correspondence is effective for computing Gromov-Witten invariants in this context.
- Quiver flag zero loci are a rich source of Fano manifolds.
- The findings expand the landscape of known Fano manifolds and their properties.
Keywords:
Fano manifoldsPicard–Fuchsequationsmirror symmetryquantum differential equationsquiver flag varietiesMore Related Videos
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