Gemetry Seminar - 28 February 2020 ,
from 15:15 to 16:15 in room D'Antoni

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Laura Pertusi 
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Universita' di Milano
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Stability Conditions on Gushel-Mukai varieties
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A generic Gushel-Mukai variety X is a quadric section of a linear section of the Grassmannian Gr(2,5). Kuznetsov and Perry proved that the bounded derived category of X has a semiorthogonal decomposition with exceptional objects and a non-trivial subcategory Ku(X), known as the Kuznetsov component. In this talk we will discuss the construction of stability conditions on Ku(X) and, consequently, on the bounded derived category of X. As applications, for X of even-dimension, we will construct locally complete families of hyperkaehler manifolds from moduli spaces of stable objects in Ku(X) and we will determine when X has a homological associated K3 surface. This is a joint work with Alex Perry and Xiaolei Zhao.