Graduate Computational Algebraic Geometry Seminar
Luke Oeding
University of Florence
Toward a salmon conjecture
Abstract: By using a result from the numerical algebraic geometry package
Bertini we show that (with extremely high probability) a set of degree
six and degree nine polynomials cut out the secant variety
$\sigma_{4}(\mathbb P^{2}\times\mathbb P^{2}\times\mathbb P^{3})$. This, combined
with an argument provided by Lansberg and Manivel, implies
set-theoretic defining equations for a much larger set of secant
varieties, including $\sigma_{4}(\mathbb P^{3}\times\mathbb P^{3}\times\mathbb P^{3})$
which is of particular interest in light of the salmon prize
offered by E. Allman for the ideal-theoretic defining equations. Our
equations are in lower degree than Friedland's March 2010 solution to
the set-theoretic problem, and thus can be seen as a starting point
for the ideal-theoretic problem.
I will describe our polynomials and some of their symmetry. Then I
will outline our geometric argument. Finally I will discuss the
results from Bertini which solve the set-theoretic problem.
Thursday October 7, 2010 at 10:00 AM in SEO 1227