Towards a new technique to compute the Orlov spectrum

Abstract: A generator of a triangulated category is an object from which we can obtain the whole category through certain operations. Associated to a generator, there is the notion of the generation time, which is the number describing how long the rebuilding process takes. The generation time of the fastest generator is called the Rouquier dimension of the category and it is conjectured that the Rouquier dimension of the derived category of a smooth projective variety of dimension $n$ is exactly $n$. Orlov suggested that in order to extract additional geometric information from the category, one should study all possible generation times – the Orlov spectrum. Later, Ballard, Favero, and Katzarkov developed considerably our understanding of the topic, making connections to rationality, computing the Orlov spectrum in several cases and finding bounds for it. In this talk, we will review part of their results and discuss our work in progress on a new technique to compute the Orlov spectrum, which takes inspiration on Abouzaid's criterion for generating the Fukaya category in terms of open-closed maps.

Mathematics

Audience: researchers in the topic

Seminario de Geometría y Física - Matemática UCN-USP