A characteristic free approach to secant varieties of triple Segre products

Abstract

The goal of this short note is to study the secant varieties of the triple Segre product of type (1,a,b) by means of the standard tools of combinatorial commutative algebra. We reprove and extend to arbitrary characteristic results of Landsberg and Weyman regarding the defining ideal and the Cohen-Macaulay property of the secant varieties. Furthermore for these varieties we compute the degree and give a bound for their Castelnuovo-Mumford regularity which is sharp in many cases.

arXiv commentTypos corrected. After the paper was published we came to know that our results have some overlap with the paper "Gröbner bases and the Cohen-Macaulay property of Li's double determinantal varieties" by Fieldsteel, Nathan; Klein, Patricia arXiv:1906.06817 published in Proc. Amer. Math. Soc. Ser. B 7 (2020), 142--158