Abstract:

Geometric invariants are a concept coming from differential geometry,
appearing in a very natural way, which can be used in algebraic
geometry. They provide new geometric insight into the local behavior of
algebraic varieties.

The geometric invariants of curves have been already classified and
understood well, to the point that we already know how to use them to
solve the problem of resolution of curve singularities, which was
originally of purely algebraic nature, in a more geometric and
differential way. Drawing inspiration from the curve case, the geometric
invariants of surfaces should again help to better understand the
problem of resolution of singularities in the surface case which is
highly nontrivial and of basic importance.

This talk will give an introduction to the concept of geometric
invariants of surfaces. We will introduce a minimal system of generators
for the field of geometric invariants of surfaces and will illustrate
why they appear naturally.