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 2 or 3-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 “Hyperkahler Geometry”, Bonn, September 6–10, 2021.
Kernels of categorical resolutions of nodal singularities / Cattani, Warren; Giovenzana, Franco; Liu, Shengxuan; Magni, Pablo; Martinelli, Luigi; Pertusi, Laura; Song, Jieao. - In: RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO. - ISSN 0009-725X. - 72:6(2023), pp. 3077-3105. [10.1007/s12215-023-00895-3]
Kernels of categorical resolutions of nodal singularities
Cattani, Warren;
2023-01-01
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 2 or 3-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 “Hyperkahler Geometry”, Bonn, September 6–10, 2021.| File | Dimensione | Formato | |
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