Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: Canonical strip hypotheses for orbifolds

Seminar | November 27 | 5-6 p.m. | 939 Evans Hall

 Ben Wormleighton, UC Berkeley

 Department of Mathematics

The Hilbert polynomial of a polarised variety is a well-studied invariant, but one that has many more secrets to give up. In 2009 Golyshev shared some insight into the structure of the roots of the Hilbert polynomial of a smooth Fano variety, inspired by work of Rodriguez-Villegas on generating functions, Yau on constraints for characteristic classes, and by several others on roots of Ehrhart polynomials. The shape of the results proven and conjectured in these papers became known as ‘canonical strip hypotheses’. I will outline these hypotheses, share recent counterexamples due to Belmans, Galkin, and Mukhopadhyay, and describe some of my recent work in extending these hypotheses to the orbifold setting.