Homological mirror symmetry of elementary birational cobordisms
Gabriel Kerr
TL;DR
This paper proves homological mirror symmetry for certain birational cobordisms, showing an equivalence between derived categories of coherent sheaves and Fukaya-Seidel categories of mirror potentials with symmetrical structures.
Contribution
It establishes the homological mirror symmetry conjecture for elementary birational cobordisms such as weighted projective spaces and stacky blow-ups.
Findings
Homological mirror symmetry is proven for these cobordisms.
The mirror potentials exhibit significant symmetry in their structure.
An explicit equivalence between categories is constructed.
Abstract
The derived category of coherent sheaves associated to a birational cobordism which is either a weighted projective space, a stacky Atiyah flip, or a stacky blow-up of a point has a conjectural mirror Fukaya-Seidel category . The potential defining has base and exhibits a great deal of symmetry. This paper investigates the structure of the Fukaya-Seidel category for the mirror potentials. A proof of homological mirror symmetry for these birational cobordisms is then given.
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