# Algebraic Geometry Seminar

#### 1-cycles and arithmetic of weighted complete intersections

**Speaker:**
Cristian Minoccheri, Stony Brook University

**Location:**
Warren Weaver Hall 317

**Date:**
Tuesday, February 13, 2018, 3:30 p.m.

**Synopsis:**

The geometry and arithmetic of Fano varieties depend on the geometry of low degree rational curves on them; for 2-Fano varieties (i.e. such that ch_2(X) is positive) this relation is even stronger. While no complete classification of 2-Fano varieties is known, many examples arise as low degree smooth weighted complete intersections, which include cyclic covers of projective space. I will discuss how, for this class of examples, the 2-Fano condition implies that the Chow group of 1-cycles is rather simple. Time permitting, I will also discuss how it implies that weighted complete intersections over function fields of curves satisfy weak approximation at all places and have only one R-equivalence class.