Generating the Fukaya categories of compact toric varieties
Abstract
Let $X$ be a compact toric variety. The quantum cohomology of $X$ decomposes as a direct sum, and associated to each summand $Q$ is a toric fibre $L_Q$ with rank $1$ local system. By building an explicit twistedcomplexlike object, we show that on $Q$ the KodairaSpencer isomorphism of FukayaOhOhtaOno factors through the closedopen string map to the Hochschild cohomology of $L_Q$. We deduce that the latter is injective and hence, assuming an appropriate version of Abouzaid's criterion, that $L_Q$ split generates the corresponding summand of the Fukaya category.
 Publication:

arXiv eprints
 Pub Date:
 April 2018
 arXiv:
 arXiv:1804.06386
 Bibcode:
 2018arXiv180406386S
 Keywords:

 Mathematics  Symplectic Geometry;
 53D37;
 14M25
 EPrint:
 19 pages, comments welcome