Seminar on Arithmetic Algebraic Geometry: Moduli of stable pairs, each consisting of a cubic and a line in P2

2012-11-15 14:00 - 2012-11-15 16:00
Faculty of Science Building #3 Room 413
Iku Nakamura
There are three relevant moduli spaces, geometric compactifications
$SQ_{g,K}$ and $SQ^{\toric}_{g,K}$ of the moduli of abelian varieties (Nakamura1999,
Nakamura2010), and Alexeev's complete moduli $\barAP_{g,d}$  of generalized abelian
varieties, each with a semiabelian group action and an ample divisor  (Alexeev2002).
First we review the relationship between these complete moduli spaces.
Next, we discuss a typical case dimension one and degree three.
In this case,  $SQ_{1,3}=SQ^{\toric}_{1,3}$ : the moduli of Hesse  cubics,
$\barAP_{1,3}$ : Alexeev's complete moduli of semiabelic pairs, each of a cubic
and a line. In addition we have $\barP_{1,3}$c the complete ''moduli'' of
GIT-semistable pairs, each of a cubic and a line. We compare these.