Alladi Ramakrishnan Hall

Counting Curves via Topology

Ritwik Mukherjee

IMSc

The general goal of enumerative geometry is to count how many
geometric objects are there that satisfy certain conditions. The simplest
example is ``How many lines pass through two
distinct points?'' A more interesting example is:
``How many lines are there in three dimensional
space that intersect four generic lines?''


In this talk we will describe a topological
method to approach problems in enumerative geometry.
We will use this approach to solve
concrete questions in enumerative geometry.
In particular we will try to count how many degree
d curves are there in CP^2 (the two dimensional complex projective space)
that pass through certain number of points and
have certain singularities