We prove new height inequalities for determinantal ideals in a regular local ring, or more generally in a local ring of given embedding codimension. Our theorems extend and sharpen results of Faltings and Bruns. Introduction. Let φ be a map of vector bundles on a variety X. A wellknown theorem of Eagon and Northcott [EN] gives an upper bound for the codimension of the locus where φ has rank ≤ s...

We define higher polyhedral K-groups for commutative rings, starting from the stable groups of elementary automorphisms of polyhedral algebras. Both Volodin’s theory and Quillen’s + construction are developed. In the special case of algebras associated with unit simplices one recovers the usual algebraic K-groups, while the general case of lattice polytopes reveals many new aspects, governed by...

using satellite altimetry derived mean sea level (msl), geopotential coefficients in terms of ellipsoidal harmonics from recent satellite gravimetry missions, gravity potential values over a grid consisting of 33,486 points at global sea areas are computed and the mean value of the gravity potential at msl is calculated as a new geoid’s potential value. in this way we have exactly followed the ...

We compute the canonical class of certain Rees algebras. Our formula generalizes that of Herzog and Vasconcelos. Its proof relies on the fact that the formation of the canonical module commutes with subintersections in important cases. As an application we treat the classical determinantal ideals and the corresponding algebras of minors. A considerable part of Wolmer Vasconcelos’ work has been ...

We describe some of the determinantal ideals attached to symmetric, exterior and tensor powers of a matrix. The methods employed use elements of Zariski’s theory of complete ideals and of representation theory. Let R be a commutative ring. The determinantal ideals attached to matrices with entries in R play ubiquitous roles in the study of the syzygies of R–modules. In this note, we describe so...

We overview results from our experiment of merging two seemingly unrelated disciplines – higher algebraic K-theory of rings and the theory of lattice polytopes. The usual K-theory is the “theory of a unit simplex”. The text is based on the works [BrG1, BrG5, BrG6]. Further related results are found in [BrG2, BrG3, BrG4]. At the end of the paper we propose a general conjecture on the structure o...

Using satellite altimetry derived mean sea level (MSL), geopotential coefficients in terms of ellipsoidal harmonics from recent satellite gravimetry missions, gravity potential values over a grid consisting of 33,486 points at global sea areas are computed and the mean value of the gravity potential at MSL is calculated as a new geoid’s potential value. In this way we have exactly followed the ...

Introdução: A síndrome de Bruns é uma manifestação rara neurocisticercose (NCC) intraventricular. NCC causada pela larva da Tenia solium, por meio contaminação fecal-oral, e caracteriza-se como das possíveis infecções helmínticas do sistema nervoso central. doença possui maior prevalência em países baixa renda, onde há precariedade no saneamento básico, além ser causas convulsões mundo. Apresen...