Unwinding toric degenerations and mirror symmetry for Grassmannians
Abstract
The most fundamental example of mirror symmetry compares the Fermat hypersurfaces in P^n and P^n/G, where G is a finite group that acts on P^n and preserves the Fermat hypersurface. We generalise this to hypersurfaces in Grassmannians, where the picture is richer and more complex. There is a finite group G that acts on the Grassmannian Gr(n,r) and preserves an appropriate CalabiYau hypersurface. We establish how mirror symmetry, toric degenerations, blowups and variation of GIT relate the CalabiYau hypersurfaces inside Gr(n,r) and Gr(n,r)/G. This allows us to describe a compactification of the EguchiHoriXiong mirror to the Grassmannian, inside a blowup of the quotient of the Grassmannian by G.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.07273
 Bibcode:
 2021arXiv211007273C
 Keywords:

 Mathematics  Algebraic Geometry;
 14J33 (Primary) 14M15;
 52B20 (Secondary)
 EPrint:
 34 pages