Algebraic Geometry Seminar: A smooth space of stable maps and a conjecture of Abramovich--Fantechi

  • Date: 01/18/2010
Jonathan Wise (UBC)

University of British Columbia


The stack of stable maps parameterizes maps from a complete curves
having at worst nodal singularities into a smooth scheme.  Generally
this stack is not smooth, but we will explain how it can be made smooth
by relaxing the condition that the source curves be complete.  Although
the resulting stack is not fibered in groupoids, and therefore may not
be easily accessible to geometric intuition, it is a natural setting in
which to construct the virtual fundamental class.  We will discuss how
this generalization can be used to prove a conjecture of Abramovich and
Fantechi relating the virtual fundamental classes of two different
moduli spaces parameterizing stable maps into mildly singular schemes.


3:10pm-4:30pm, WMAX 110