Lagrangian Floer theory for trivalent graphs and homological mirror symmetry for curves
Abstract
Mirror symmetry for higher genus curves is usually formulated and studied in terms of LandauGinzburg models; however the critical locus of the superpotential is arguably of greater intrinsic relevance to mirror symmetry than the whole LandauGinzburg model. Accordingly, we propose a new approach to the Amodel of the mirror, viewed as a trivalent configuration of rational curves together with some extra data at the nodal points. In this context, we introduce a version of Lagrangian Floer theory and the Fukaya category for trivalent graphs, and show that homological mirror symmetry holds, namely, that the Fukaya category of a trivalent configuration of rational curves is equivalent to the derived category of a nonArchimedean generalized Tate curve.
 Publication:

arXiv eprints
 Pub Date:
 July 2021
 arXiv:
 arXiv:2107.01981
 Bibcode:
 2021arXiv210701981A
 Keywords:

 Mathematics  Symplectic Geometry;
 Mathematics  Algebraic Geometry
 EPrint:
 52 pages, 6 figures