Algebraic and Arithmetic Geometry Seminar
# Tautological classes on the relative Picard scheme

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Europe/Rome

Aula Seminari (Department of Mathematics)
### Aula Seminari

#### Department of Mathematics

Description

Intersection theory of the moduli space $M_g$ of genus $g$ stable curves has been an active area of research. Extending this subject, one can consider a relative moduli stack of rank $r$ bundles over the moduli space $M_g$ which is a smooth algebraic stack. What can we say about the intersection theory of this moduli stack? In this talk, I will focus on the relative Picard scheme over Mg (rank 1 case) and give two methods to study the tautological ring of relative Picard schemes. The first approach arises from studying double ramification cycles. This direction is joint work with D. Holmes, R. Pandharipande, J. Schmitt and R. Schwarz. The second approach involves a certain construction of Quot schemes over the relative Picard scheme. This gives a quasi-map type moduli spaces for quotient stacks $[\mathsf{Grass}(r,N)/G_m]$. This direction is work in progress with H. Lho.