The cohomology table of coherent sheaves on singular projective varieties

Abstract: The cohomology table of a coherent sheaf on a projective variety is numerical data of the dimension of each cohomoogy group of each twist of the sheaf. Eisenbud--Schreyer give a description of the cone of cohomology table of vector bundles and coherent sheaves on projective spaces. This leads to their proof of the Boij--Soderberg theory which describes the cone spanned by the Betti tables of graded modules over polynomial rings. In this talk, we give some extensions of these results of Eisenbud--Schreyer to singular projective varieties and singular standard graded rings. Our central technique is to use a sequence of coherent sheaves that behave like an Ulrich sheave asymptotically. We call such sequence a lim Ulrich sequence of sheaves and we can prove their existence in positive characteristic. This talk is largely based on joint work in progress with Srikanth Iyengar and Mark Walker.

algebraic geometry

Audience: researchers in the topic

ZAG (Zoom Algebraic Geometry) seminar

Series comments: Description: ZAG seminar

The seminar takes place on Tuesdays and Thursdays via Zoom. Zoom passwords are given via mailing list on Fridays. To join the mailing list go to the website.

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