Séminaire de géométrie algébrique

Virt: Francesca Carocci: A modular smooth compactification of genus 2 curves in projective spaces

001 (batiment I)


batiment I

Département de mathématiques Bâtiment I Faculté des Sciences 2 Boulevard Lavoisier F-49045 Angers cedex 01 France
Moduli spaces of stable maps in genus bigger than zero  include many components of different dimensions meeting each other in complicated ways, and the closure of the smooth locus is difficult to describe. We will look at examples of genus one and two maps of low degree in the projective plane to get a feeling of how complicated these spaces can be.
Afterwords, we will sketch the construction of a modular desingularization of the space of genus 2 maps to projective spaces using combinatorial techniques from tropical geometry and maps from certain exotic  curve singularities.