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)