Orlov spectra: bounds and gaps
By Matthew R. Ballard, David Favero, L. Katzarkov. 2010
71 citations recorded by the source corpus.
The Orlov spectrum is a new invariant of a triangulated category. It was introduced by D. Orlov, building on work of A. Bondal-M. Van den Bergh and R. Rouquier. The supremum of the Orlov spectrum of a triangulated category is called the ultimate dimension. In this work, we study Orlov spectra of triangulated categories arising in mirror symmetry. We introduce the notion of gaps and outline their geometric significance. We provide the first large class of examples where the ultimate dimension is finite: categories of singularities associated to isolated hypersurface singularities. Similarly, given any nonzero object in the bounded derived category of coherent sheaves on a smooth Calabi-Yau hypersurface, we produce a generator, by closing the object under a certain monodromy action, and uniformly bound this generator’s generation time. In addition, we provide new upper bounds on the generation times of exceptional collections and connect generation time to braid group actions to provide a lower bound on the ultimate dimension of the derived Fukaya category of a symplectic surface of genus greater than one.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/8797227a8f6c5d72fcec5fc64d8a18594551d03b
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In Geometry and Topology
- Matthew R. Ballard
- David Favero
- L. Katzarkov
- P. Seidel
- D. Auroux
- Yankı Lekili
- Dmitri Orlov
- M. Abouzaid
In Mathematical Physics
Citations in the corpus
- A category of kernels for equivariant factorizations and its implications for Hodge theory (2011, methodology): “ogonal decompositions of triangulated dg-categories we shall always implicitly mean their homotopy categories but suppress this from the discussion, see the appendix to [CT10] for details on this. In [BFK10], an in depth analysis of the relationship between generation time and semiorthogonal decompo”