Derived projectivizations and Grassmannians and their applications

Abstract: We will explore some applications of the Derived Algebraic Geometry (DAG), a powerful framework developed by Toen-Vezzosi, Lurie and many others. DAG allows us to extend Grothendieck’s theory of projectivizations and Grassmannians of sheaves to the cases of complexes. This derived extension is very useful for constructing and studying moduli spaces, especially when the spaces are singular and difficult to analyze in the classical framework. We will discuss the constructions of derived projectivizations and Grassmannians as well as their properties, with a focus on their applications to Abel maps for singular curves and Hecke correspondences for smooth surfaces. Based on papers arXiv:2202.11636 and arXiv:2212.10488 and works in preparation.

algebraic geometryrepresentation theory

Audience: researchers in the topic

Algebra and Geometry Seminar @ HKUST

Series comments: Algebra and Geometry seminar at the Hong Kong University of Science and Technology (HKUST).

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