Homological mirror symmetry of elementary birational cobordisms
Abstract
The derived category of coherent sheaves TB 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 TA. The potential W defining TA has base C* 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 TA TB for these birational cobordisms is then given.
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