Search arXiv⌕ Search

arXiv · math/0601097

Generalizations of Strassen's equations for secant varieties of Segre varieties

Abstract

We define many new examples of modules of equations for secant varieties of Segre varieties that generalize Strassen's commutation equations. Our modules of equations are obtained by constructing subspaces of matrices from tensors that satisfy various commutation properties.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

J. M. Landsberg, L. Manivel. 2006-01-05. Generalizations of Strassen's equations for secant varieties of Segre varieties. https://arxiv.org/abs/math/0601097

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Good minimal models with nowhere vanishing holomorphic $1$-forms

Popa and Schnell show that any holomorphic 1-form on a smooth projective variety of general type has zeros. In this article, we show that a smooth good minimal model has a holomorphic 1-form without zero if and only if it admits an analytic fiber bundle structure over a positive dimensional abelian variety.

math.AG↗

Algebraic Zhou valuations

In this paper, we generalize Zhou valuations, originally defined on complex domains, to the framework of general schemes. We demonstrate that an algebraic version of the Jonsson--Mustaţă conjecture is equivalent to the statement that every Zhou valuation is quasi-monomial. By introducing a mixed version of jumping numbers and Tian functions associated with valuations, we obtain characterizations of a valuation being a Zhou valuation or computing some jumping number using the Tian functions. Furthermore, we establish the correspondence between Zhou valuations in algebraic settings and their counterparts in analytic settings.

math.AG↗