Serre functors and dimensions of residual categories
arXiv:2109.02026
Abstract
We describe in terms of spherical twists the Serre functors of many interesting semiorthogonal components, called residual categories, of the derived categories of projective varieties. In particular, we show the residual categories of Fano complete intersections are fractional Calabi--Yau up to a power of an explicit spherical twist. As applications, we compute the Serre dimensions of residual categories of Fano complete intersections, thereby proving a corrected version of a conjecture of Katzarkov and Kontsevich, and deduce the nonexistence of Serre invariant stability conditions when the degrees of the complete intersection do not all coincide.
arXiv comment53 pages, minor updates
References in corpus (12)
- Derived categories of cubic fourfolds
- Base change for semiorthogonal decompositions
- New derived symmetries of some hyperkähler varieties
- Stability conditions on Kuznetsov components
- Stability conditions in families
- Grothendieck Duality for Deligne-Mumford Stacks
- Stability conditions and moduli spaces for Kuznetsov components of Gushel-Mukai varieties
- The desingularization of the theta divisor of a cubic threefold as a moduli space
- Moduli spaces on the Kuznetsov component of Fano threefolds of index 2
- Some remarks on Fano threefolds of index two and stability conditions
- Bridgeland Moduli spaces for Gushel-Mukai threefolds and Kuznetsov's Fano threefold conjecture
- Perverse schobers and the Algebra of the Infrared