
details
Title
Compactified Picard stacks over the moduli space of curves with marked points
Abstract Let $X$ be a projective curve of genus $g$ and $Pic^d(X)$ its degree $d$
Picard variety, parameterizing isomorphism classes of invertible
sheaves of degree $d$ on $X$.
$Pic^d(X)$ is a very important invariant of the curve and it is well
known that it is complete if and only if $X$ is a curve of compact type.
The problem of compactifying $Pic^d(X)$ has been widely studied in the
last decades and nowadays there are several solutions, differing
from one another in various aspects such as the geometrical interpretation
or the functorial properties.
By the other hand, the introduction of (algebraic) stacks in the study of
moduli problems in algebraic geometry allowed a deeper understanding of
the objects one wants to parametrize exactly because of the good functorial
properties of moduli stacks.
In the first part of my talk I will explain how to construct
geometrically meaningful algebraic (Artin) stacks $\overline{\mathcal
P}_{d,g}$ over the moduli stack of stable curves, $\overline{\mathcal
M}_g$, giving a functorial way of compactifying the relative degree $d$ Picard
variety for families of stable curves.
In the secont part, I will explain how to generalize this construction to
curves with marked points using an inductive argument that consists, at
each step, on giving a geometrical description of the universal family
over the previous stack.
Speaker(s)
Ana Margarida Melo (CMUC/Mat. FCTUC and Università Roma Tre)
Date
December 22, 2008 Time 15.00 Room
Sala 5.5

