Exceptional collections for invertible polynomials using VGIT

Abstract: A sum of n monomials in n variables is said to be invertible if it is quasi-homogeneous and quasi-smooth (i.e. it has a unique singularity at the origin). To an invertible polynomial w, one can associate a maximal symmetry group, and consider the derived category of equivariant matrix factorizations of w. Joint with David Favero and Tyler Kelly, we prove this category has a full exceptional collection, using a variation of GIT result of Ballard—Favero—Katzarkov. Our proof additionally utilizes the Kreuzer-Skarke classification of invertible polynomials as Thom—Sebastiani sums of Fermat, chain, and loop polynomials. I’ll present a friendly, example-oriented illustration of our approach, review related literature, and discuss applications to mirror symmetry.

algebraic geometrycombinatorics

Audience: researchers in the topic

( slides | video )

---

Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html

---