Secant Cumulants and Secant variety of the Segre product

10 July,2019
Versione stampabile
Venue: Seminar Room “-1” – Department of Mathematics – Via Sommarive, 14 Povo - Trento
Time: 9.00 a.m.
 
Claudia De Lazzari - PhD in Mathematics
 
Abstract: 
The secant variety of the Segre embedding has been studied classically and there is current interest in the topic due to the wide variety of applications. We present a different method which derives from applications of toric techniques in Algebraic Statistics and Phylogenetics and based on secant cumulants. Secant cumulants give a purpose-built coordinate system on the projective space. In this talk we will focus our attention on the secant of the Segre product of projective lines as the prototypical case, i.e. $X = Sec((P^1)^{×n})$.
In particular secant cumulants enable to explicitly provide a covering of X with affine toric varieties which are defined by quadratic binomials. According to the presented approach, the secant cumulant coordinates represent an alternative tool for studying the ideal of these secant varieties and, in addition, they highlight their geometrical toric structure.
 
The seminar corresponds to the final exam of Algebraic Geometry II, a planned course within  De Lazzari's  first year PHD study programme  
 
Contact Person: Eduardo Luis Sola Conde