Homological mirror symmetry of elementary birational cobordisms

• Gabriel Kerr ^[1]
  1. [1] Kansas State University

     Kansas State University

     City of Manhattan, Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 23, Nº. 4, 2017, págs. 2801-2847
• Idioma: inglés
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• Resumen

  • 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.