**Venue**: Seminar Room “-1” – Department of Mathematics – Via Sommarive, 14 Povo - Trento

**Time**: 9.45 a.m.

Reynaldo Staffolani - PhD in Mathematics

**Abstract**:

Given a non degenerate irreducible projective variety $X$, its $2$-secant variety is defined as the Zariski closure of the union of the spans of any two points of the variety $X$.

The aim of this talk is to study the $2 $-secant variety of some well known toric varieties.

In particular, given an $n$-dimensional smooth lattice polytope $P \subset 2 \Delta_n $, we will show that up to $AGL _n(\mathbb{Z})$-equivalence, it is one of $$\Delta_n,\quad 2\Delta_n,\quad(2\Delta_n)_k \; 0\leq k \leq n-2, \quad \Delta_l \times \Delta_{n-l}\; 1\leq l \leq n-1.$$

We will describe its corresponding toric variety $X_P $ and we will compute the dimension of its $2 $-secant variety.

The seminar corresponds to the final exam of Algebraic Geometry II, a planned course within Staffolani's first year PHD study programme

**Contact Person**: Eduardo Luis Sola Conde