Algebraic Geometry Seminar
Aaron Landesman
Harvard University
Interpolation of Projective Varieties
Abstract: In this talk, we discuss interpolation of projective varieties through points.
It is well known that one can find
a rational normal curve in $\mathbb P^n$
through $n+3$ general points. More recently, it
was shown that one can always find nonspecial curves
through the expected number of general points.
We consider the generalization of this question
to varieties of all dimensions and explain why
rational normal scrolls satisfy interpolation.
We'll also discuss joint work
with Anand Patel on interpolation for del Pezzo surfaces
and present several interesting open interpolation problems.
We'll place particular emphasis on explaining the standard techniques used
to solve interpolation:
deformation theory, specialization, degeneration, and association.
Monday February 15, 2016 at 2:00 PM in SEO 1227