Secant varieties of toric varieties part 2

July 10, 2019
Versione stampabile
Venue: Seminar Room “-1” – Department of Mathematics – Via Sommarive, 14 Povo - Trento
Time: 10.30 a.m.
 
Pierpaola Santarsiero - 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 $X$. \\Given an $n$-dimensional smooth lattice polytope $P \subset \mathbb{R}^n $ not $AGL _n(\mathbb{Z})$-equivalent to $\Delta_n$, $2\Delta_n$,
$(2\Delta_n)_k $ for $ 0\leq k \leq n-2$ or to $ \Delta_l \times \Delta_{n-l}$ for $ 1\leq l \leq n-1$, then the generic point of its $2 $-secant variety is identifiable, i.e. it lies on an unique secant line of $X_P $. This concludes the study of the dimension of the $2 $-secant variety of a variety associated to a smooth $n$-dimensional lattice polytope.
 
The seminar corresponds to the final exam of Algebraic Geometry II, a planned course within  Santarsiero's  first year PHD study programme  
 
Contact Person: Eduardo Luis Sola Conde