Universality of High-Strength Tensors

Autor: Arthur Bik, Rob H. Eggermont, Alessandro Danelon, Jan Draisma

Publikováno v: Vietnam Journal of Mathematics, 50(2), 557-580. Springer
Bik, Arthur; Danelon, Alessandro; Draisma, Jan; Eggermont, Rob H (2022). Universality of High-Strength Tensors. Vietnam journal of mathematics, 50(2), pp. 557-580. Springer 10.1007/s10013-021-00522-7

A theorem due to Kazhdan and Ziegler implies that, by substituting linear forms for its variables, a homogeneous polynomial of sufficiently high strength specialises to any given polynomial of the same degree in a bounded number of variables. Using e

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d8fd1a56f2bf51f0eeb448d25d33ea70
https://research.tue.nl/en/publications/07c10229-3e84-466d-92f2-21faa4bc312b

Plücker varieties and higher secants of Sato’s Grassmannian

Autor: Rob H. Eggermont, Jan Draisma

Publikováno v: Journal für die reine und angewandte Mathematik, 189-215. Walter de Gruyter GmbH
ISSUE=737;STARTPAGE=189;ENDPAGE=215;ISSN=0075-4102;TITLE=Journal für die reine und angewandte Mathematik

Every Grassmannian, in its Plücker embedding, is defined by quadratic polynomials. We prove a vast, qualitative, generalisation of this fact to what we call Plücker varieties. A Plücker variety is in fact a family of varieties in exterior powers o

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f1e44b8f0f85e5764f3e160c31d085c0
https://doi.org/10.1515/crelle-2015-0035

Noetherianity for infinite-dimensional toric varieties

Autor: Rob H. Eggermont, Anton Leykin, Jan Draisma, Robert Krone

Publikováno v: Draisma, J, Eggermont, R H, Krone, R & Leykin, A 2015, ' Noetherianity for infinite-dimensional toric varieties ', Algebra & Number Theory, vol. 9, no. 8, pp. 1857-1880 . https://doi.org/10.2140/ant.2015.9.1857
Algebra & Number Theory, 9(8), 1857-1880. Mathematical Sciences Publishers
Algebra Number Theory 9, no. 8 (2015), 1857-1880

We consider a large class of monomial maps respecting an action of the infinite symmetric group, and prove that the toric ideals arising as their kernels are finitely generated up to symmetry. Our class includes many important examples where Noetheri

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e923a399e3db26d2622ad66b4f473214
https://doi.org/10.2140/ant.2015.9.1857

Topological noetherianity for cubic polynomials

Autor: Andrew Snowden, Harm Derksen, Rob H. Eggermont

Publikováno v: Algebra Number Theory 11, no. 9 (2017), 2197-2212
Algebra & Number Theory, 11(9), 2197-2212. Mathematical Sciences Publishers

Let $P_3(\mathbf{C}^{\infty})$ be the space of complex cubic polynomials in infinitely many variables. We show that this space is $\mathbf{GL}_{\infty}$-noetherian, meaning that any $\mathbf{GL}_{\infty}$-stable Zariski closed subset is cut out by fi

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::78a138c77af303fa10d5c9585d24a212
https://projecteuclid.org/euclid.ant/1513730352

Algebraic boundary of matrices of nonnegative rank at most three

Autor: Kaie Kubjas, Rob H. Eggermont, Emil Horobeţ

Publikováno v: Linear Algebra and Its Applications, 508, 62-80. Elsevier

The Zariski closure of the boundary of the set of matrices of nonnegative rank at most 3 is reducible. We give a minimal generating set for the ideal of each irreducible component. In fact, this generating set is a Grobner basis with respect to the

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::23f73389f017360efd672da5faa7d814
http://arxiv.org/abs/1412.1654