Speaker: Cristina Manolache
Title: A method for comparing Gromov-Witten-like invariants.
Abstract:
For a (special) variety X we can construct several compact spaces of curves on
X which are nice enough to allow us do intersection theory on them.
Intersection theory on these different compactifications gives rise to several
types of invariants: Gromov-Witten invariants, stable quotient invariants,
stable quasi-maps invariants, etc. Very roughly (and naively), we might think
of a Gromov-Witten invariant, or a stable quotient invariant, etc, as the
number of curves on X of fixed genus, fixed degree and which intersect some
given subvarieties of X. In particular, we might expect the above invariants to
be equal. There are by now several theorems and conjectures which relate these
different types of invariants.
In this seminar I will define Gromov-Witten invariants and stable quotient
invariants and prove that they are equal. If time allows I will also discuss
some features which appear in the more general picture.