Kite, Alex;
Segal, Ed;
(2022)
Discriminants and Semi-orthogonal Decompositions.
Communications in Mathematical Physics
, 390
(2)
pp. 907-931.
10.1007/s00220-021-04298-2.
Preview |
Text
Segal_s00220-021-04298-2.pdf Download (494kB) | Preview |
Abstract
The derived categories of toric varieties admit semi-orthogonal decompositions coming from wall-crossing in GIT. We prove that these decompositions satisfy a Jordan–Hölder property: the subcategories that appear, and their multiplicities, are independent of the choices made. For Calabi–Yau toric varieties wall-crossing instead gives derived equivalences and autoequivalences, and mirror symmetry relates these to monodromy around the GKZ discriminant locus. We formulate a conjecture equating intersection multiplicities in the discriminant with the multiplicities appearing in certain semi-orthogonal decompositions. We then prove this conjecture in some cases.
| Type: | Article |
|---|---|
| Title: | Discriminants and Semi-orthogonal Decompositions |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00220-021-04298-2 |
| Publisher version: | https://doi.org/10.1007/s00220-021-04298-2 |
| Language: | English |
| Additional information: | This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. |
| UCL classification: | UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics UCL > Provost and Vice Provost Offices > UCL BEAMS UCL |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10142804 |
Archive Staff Only
 |
View Item |
