27 research outputs found
Binomial generation of the radical of a lattice ideal
Let be a lattice ideal. We provide a necessary and sufficient
criterion under which a set of binomials in generate the radical
of up to radical. We apply our results to the problem of
determining the minimal number of generators of or of the
up to radical.Comment: 14 pages, to appear in Journal of Algebr
On the binomial arithmetical rank of lattice ideals
To any lattice one can associate the lattice ideal
. This paper concerns the study of the
relation between the binomial arithmetical rank and the minimal number of
generators of . We provide lower bounds for the binomial arithmetical
rank and the -homogeneous arithmetical rank of .
Furthermore, in certain cases we show that the binomial arithmetical rank
equals the minimal number of generators of . Finally we consider a class
of determinantal lattice ideals and study some algebraic properties of them.Comment: 22 page
Minimality of toric arrangements
We prove that the complement of a toric arrangement has the homotopy type of a minimal CW-complex. As a corollary we deduce that the integer cohomology of these spaces is torsionfree.We apply discrete Morse theory to the toric Salvetti complex, providing a sequence of cellular collapses that leads to a minimal complex
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Geometric and Topological Combinatorics
The 2007 Oberwolfach meeting “Geometric and Topological Combinatorics” presented a great variety of investigations where topological and algebraic methods are brought into play to solve combinatorial and geometric problems, but also where geometric and combinatorial ideas are applied to topological questions
Arithmetical rank of binomial ideals
In this paper, we investigate the arithmetical rank of a binomial ideal J. We provide lower bounds for the binomial arithmetical rank and the J-complete arithmetical rank of J. Special attention is paid to the case where J is the binomial edge ideal of a graph. We compute the arithmetical rank of such an ideal in various cases. © 2017, Springer International Publishing AG
International Congress of Mathematicians: 2022 July 6–14: Proceedings of the ICM 2022
Following the long and illustrious tradition of the International Congress of Mathematicians, these proceedings include contributions based on the invited talks that were presented at the Congress in 2022.
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