Venue
Online
Speaker
Mr. Nilkantha Das.
Affiliation
SMS, NISER
Title
Enumerative geometry of curves in a moving family of surfaces.
Abstract: Enumerative geometry of curves in the complex projective plane is very classical. In this talk, we consider two generalisations of classical enumerative geometric problems of curves in the plane. We consider curves in that lie inside a
in
; such curves are called planar curves. We discuss the enumeration of degree
planar curves in
having
nodes and another singularity of codimension
, and that intersect
generic lines and pass through
generic points in
, where
with
. We also count the number of elliptic (
) curves of degree
in a del Pezzo surface
that pass through
generic points of
.