AAG Seminar: Hodge numbers of orbifold Clarke mirrors and mirror symmetry

Abstract: Batyrev and Borisov gave a combinatorial mirror construction of dual pairs of toric complete intersections Calabi-Yau varieties coming from nef partitions of reflexive polytopes, and in 1996 they showed that the stringy Hodge numbers of these pairs satisfy a particular duality predicted by mirror symmetry. Later, Clarke gave a far-reaching combinatorial mirror construction which generalizes the Batyrev-Borisov construction and many other combinatorial mirror constructions.

I'll describe work in progress with Sukjoo Lee (Edinburgh) that uses new tools from tropical geometry to prove Hodge number duality for a large class of Clarke mirror pairs. This immediately recovers Batyrev and Borisov's results and leads to a proof of a conjecture of Katzarkov, Kontsevich, and Pantev for orbifold toric complete intersections. I'll describe how a construction of Doran and Harder, relating Laurent polynomials and singular toric complete intersections, fits into the Clarke mirror framework. As a consequence, my results with Sukjoo lead to predictions related to the Fanosearch Program.  

Host: Matt Kerr