Kernels of categorical resolutions of nodal singularities
Algebraic Geometry
2023-05-10 v2
Abstract
In this paper we study derived categories of nodal singularities. We show that for all nodal singularities there is a categorical resolution whose kernel is generated by a or -spherical object, depending on the dimension. We apply this result to the case of nodal cubic fourfolds, where we describe the kernel generator of the categorical resolution as an object in the bounded derived category of the associated degree six K3 surface. This paper originated from one of the problem sessions at the Interactive Workshop and Hausdorff School "Hyperk\"ahler Geometry", Bonn, September 6-10, 2021.
Keywords
Cite
@article{arxiv.2209.12853,
title = {Kernels of categorical resolutions of nodal singularities},
author = {Warren Cattani and Franco Giovenzana and Shengxuan Liu and Pablo Magni and Luigi Martinelli and Laura Pertusi and Jieao Song},
journal= {arXiv preprint arXiv:2209.12853},
year = {2023}
}
Comments
30 pages, final version to appear in Rendiconti del Circolo Matematico di Palermo Series 2