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Maps of toric varieties in Cox coordinates

Gavin Brown, Jarosław Buczyński (2013)

Fundamenta Mathematicae

The Cox ring provides a coordinate system on a toric variety analogous to the homogeneous coordinate ring of projective space. Rational maps between projective spaces are described using polynomials in the coordinate ring, and we generalise this to toric varieties, providing a unified description of arbitrary rational maps between toric varieties in terms of their Cox coordinates. Introducing formal roots of polynomials is necessary even in the simplest examples.

Meandering of trajectories of polynomial vector fields in the affine n-space.

Dimitri Novikov, Sergei Yakovenko (1997)

Publicacions Matemàtiques

We give an explicit upper bound for the number of isolated intersections between an integral curve of a polynomial vector field in Rn and an affine hyperplane.The problem turns out to be closely related to finding an explicit upper bound for the length of ascending chains of polynomial ideals spanned by consecutive derivatives.This exposition constitutes an extended abstract of a forthcoming paper: only the basic steps are outlined here, with all technical details being either completely omitted...

Modular deformations and space curve singularities.

Bernd Martin (2003)

Revista Matemática Iberoamericana

We investigate different concepts of modular deformations of germs of isolated singularities (infinitesimal, Artinian, formal). An obstruction calculus based on the graded Lie algebra structure of the tangent cohomology for modular dcformations is introduced. As the main result the characterisation of the maximal infinitesimally modular subgerm of the miniversal family as flattening stratum of the relative Tjurina module is extended from ICIS to space curve singularities.

Multidimensional term indexing for efficient processing of complex queries

Michal Krátký, Tomáš Skopal, Václav Snášel (2004)

Kybernetika

The area of Information Retrieval deals with problems of storage and retrieval within a huge collection of text documents. In IR models, the semantics of a document is usually characterized using a set of terms. A common need to various IR models is an efficient term retrieval provided via a term index. Existing approaches of term indexing, e. g. the inverted list, support efficiently only simple queries asking for a term occurrence. In practice, we would like to exploit some more sophisticated...

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