Quadratic families of elliptic curves and unirationality of degree 1 conic bundles

Members' Seminar
Topic:Quadratic families of elliptic curves and unirationality of degree 1 conic bundles
Speaker:János Kollár
Affiliation:Princeton University
Date:Monday, April 13
Time/Room:2:00pm - 3:00pm/S-101
Video Link:http://video.ias.edu/membersem/2015/0413-JánosKollár

We consider elliptic curves whose coefficients are degree 2 polynomials in a variable $t$. We prove that for infinitely many values of $t$ the resulting elliptic curve has rank at least 1. All such curves together form an algebraic surface which is birational to a conic bundle with 7 singular fibers. The main step of the proof is to show that such conic bundles are unirational. (joint work with M. Mella)