Arnold's seminar, 22.02.00

S.Lando "Hurwitz numbers and Hodge integrals"

A year ago I had given a talk on the same topic
on the very same seminar. During the last month
we wrote a complete proof of the result. While
writing down the proof we made use of some
tools that seemed for me to be of general interest.
Among them:

1) For a short exact sequence 0->K->E->F->0
of vector bundles their Chern classes satisfy
the relation c(E)=c(K)c(F). What can be said
about the Chern classes of the kernel and of
the cokernel bundles if we have a bundle
mapping E->F of nonconstant rank?

2) What is the Segre class of a cone bundle?

3) What are the ramification points of
a meromorphic mapping of a singular curve?

The first two of these subjects are surely
not new ones, but I believe they were not
discussed on the seminar.