Towards a new technique to compute Orlov spectra / Stability of Halphen pencils of index two

Abstract: Towards a new technique to compute Orlov spectra, by Nuno Cardoso

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.

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Stability of Halphen pencils of index two, by Aline Zanardini

Abstract: In this talk I will present some results about the stability, in the sense of geometric invariant theory, of Halphen pencils of index two under the action of SL(3). These are pencils of plane curves of degree six having nine (possibly infinitely near) base points of multiplicity two. Inspired by the work of Miranda on pencils of plane cubics, I will explain how to explore the geometry of the associated rational elliptic surfaces. I will also show that the log canonical threshold plays an important role. This work is part of my PhD thesis at the University of Pennsylvania under the supervision of Antonella Grassi.

algebraic geometry

Audience: researchers in the topic

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Brazilian algebraic geometry seminar

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