Thesis DefenseFriday August 10th, 2018 | |

Time: |
4:30 PM |

Title: |
On the Arithmetic of low degree Weighted Complete Intersections |

Speaker: |
Cristian Minoccheri, Stony Brook University |

Location: |
Math Tower 5-127 |

Abstract: | |

A variety is rationally connected if two general points can be joined by a rational curve. A higher version of this notion is rational simple connectedness, which requires suitable spaces of rational curves through two points to be rationally connected themselves. We prove that smooth, complex, weighted complete intersections of low enough degree are rationally simply connected. This result has strong arithmetic implications for weighted complete intersections defined over the function field of a smooth, complex curve. Namely, it implies that these varieties satisfy weak approximation at all places, that $R$-equivalence of rational points is trivial, and that the Chow group of zero cycles of degree zero is zero. |