# ALGEBRAIC COMBINATORICS

A characteristic free approach to secant varieties of triple Segre products
Algebraic Combinatorics, Volume 3 (2020) no. 5, pp. 1011-1021.

The goal of this short note is to study the secant varieties of the Segre embedding of the product ${ℙ}^{1}×{ℙ}^{a-1}×{ℙ}^{b-1}$ by means of the standard tools of combinatorial commutative algebra. We reprove and extend to arbitrary characteristic the results of Landsberg and Weyman [] regarding the defining ideal and the Cohen–Macaulay property of the secant varieties. Furthermore we compute their degrees and give a bound for their Castelnuovo–Mumford regularities, which are sharp in many cases.

Revised:
Accepted:
Published online:
DOI: 10.5802/alco.115
Classification: 13C40,  05E40,  13P20
Keywords: Segre products, secant varieties, Gröbner bases, tensors.
Conca, Aldo 1; De Negri, Emanuela 1; Stojanac, Željka 2

1 Dipartimento di Matematica Università di Genova via Dodecaneso 35 Genova Italy
2 Institute for Theoretical Physics University of Cologne Germany
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Conca, Aldo; De Negri, Emanuela; Stojanac, Željka. A characteristic free approach to secant varieties of triple Segre products. Algebraic Combinatorics, Volume 3 (2020) no. 5, pp. 1011-1021. doi : 10.5802/alco.115. https://alco.centre-mersenne.org/articles/10.5802/alco.115/

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