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Moduli spaces on the Kuznetsov component of Fano threefolds of index 2

Algebraic Geometry

Speaker: Matteo Altavilla, University of Utah
Related Webpage: http://www.math.utah.edu/~altavill/
Location: 2112 MSB
Start time: Wed, Jan 29 2020, 12:10PM

A Fano threefold Y of Picard rank 1 and index 2 admits a canonical semiorthogonal decomposition of its derived category; this decomposition comes with a non-trivial component Ku(Y) — called the Kuznetsov component — that encodes most of the geometry of Y. I will present a joint work with M. Petkovic and F. Rota in which we describe certain moduli spaces of Bridgeland-stable objects on Ku(Y), via the stability conditions constructed by Bayer, Macrì, Lahoz and Stellari. Furthermore, in our work we study the behavior of the Abel-Jacobi map on these moduli. As an application in the case of degree d = 2, we prove a strengthening of a categorical Torelli Theorem by Bernardara and Tabuada.