Decompositions of moduli spaces of vector bundles and graph potentials
Abstract
We propose a conjectural semiorthogonal decomposition for the derived category of the moduli space of stable rank 2 bundles with fixed determinant of odd degree, independently formulated by Narasimhan. We discuss some evidence for, and furthermore propose semiorthogonal decompositions with additional structure. We also discuss two other decompositions. One is a decomposition of this moduli space in the Grothendieck ring of varieties, which relates to various known motivic decompositions. The other is the critical value decomposition of a candidate mirror LandauGinzburg model given by graph potentials, which in turn is related under mirror symmetry to Munoz's decomposition of quantum cohomology. This corresponds to an orthogonal decomposition of the Fukaya category. We will explain how these decompositions can be seen as evidence for the conjectural semiorthogonal decomposition.
 Publication:

arXiv eprints
 Pub Date:
 September 2020
 DOI:
 10.48550/arXiv.2009.05568
 arXiv:
 arXiv:2009.05568
 Bibcode:
 2020arXiv200905568B
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Geometric Topology;
 Mathematics  Quantum Algebra;
 Mathematics  Symplectic Geometry
 EPrint:
 32 pages