筑波大学数学談話会

Image and discriminant Chern classes of stable maps

In classical algebraic geometry,
numerical characters of projective varieties
were extensively studied by means of enumerating
singular points of naturally associated maps.
A modern unified approach to such enumerative problems
is the theory of Thom polynomials based on
the classification of singularities of maps (Thom-Mather theory).
In this talk I will  introduce a new branch of the theory,
in which we replace counting singular points
by computing (weighted) Euler characteristics.
In particular, I will talk about a universal formula
on (singular) Chern class of image varieties of maps.