Displaying the cohomology of toric line bundles
Klaus Altmann (FU Berlin)
Abstract: Line bundles $L$ on projective toric varieties can be understood as formal differences $(\Delta^+ − \Delta^-)$ of convex polyhedra in the character lattice. We show how it is possible to use this language for understanding the cohomology of $L$ by studying the set-theoretic difference $(\Delta^- \setminus \Delta^+)$. Moreover, when interpreting these cohomology groups as certain Ext-groups, we demonstrate how the approach via $(\Delta^-\setminus \Delta^+)$ leads to a direct description of the associated extensions. The first part is joint work with Jarek Buczinski, Lars Kastner, David Ploog, and Anna-Lena Winz; the second is work in progress with Amelie Flatt.
algebraic geometrycombinatorics
Audience: researchers in the topic
( video )
Online Nottingham algebraic geometry seminar
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Organizers: | Alexander Kasprzyk*, Johannes Hofscheier*, Erroxe Etxabarri Alberdi |
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