Séminaire Géométries ICJ

Wall crossing morphisms for moduli of stable pairs

by Mr Giovanni Inchiostro

112 (ICJ)



1er étage bâtiment Braconnier, Université Claude Bernard Lyon 1 - La Doua
Consider a moduli space M parametrizing stable pairs of the form $(X, \sum a_i D_i)$ with $a_i$ $n$ positive rational numbers. Consider $n$ positive rational numbers $b_i$ with $b_i \le a_i$, and assume that the objects on the interior of $M$ are pairs with $K_X +\sum b_i D_i$ big. Then on the interior of $M$ one can send a pair $(X, \sum a_i D_i)$ to the canonical model of $(X, \sum b_i D_i)$. If $N$ is a moduli space of stable pairs with coefficients $b_i$ this gives a set theoretic map from an open substack of $M$ to $N$. We investigate when such a map can be extended to the whole $M$. Our main result is if the interior of $M$ parameterizes klt pairs we can extend the map, up to replacing $M$ and $N$ with their normalizations. The extension does not exist if above we replace the word normalization with seminormalizaton instead. This is joint with Kenny Ascher, Dori Bejleri and Zsolt Patakfalvi.