Search results for " 14Q15"
showing 2 items of 2 documents
Cox ring of the generic fiber
2017
Abstract Given a surjective morphism π : X → Y of normal varieties satisfying some regularity hypotheses we prove how to recover a Cox ring of the generic fiber of π from the Cox ring of X. As a corollary we show that in some cases it is also possible to recover the Cox ring of a very general fiber, and finally we give an application in the case of the blowing-up of a toric fiber space.
OPTIMIZATIONS FOR TENSORIAL BERNSTEIN–BASED SOLVERS BY USING POLYHEDRAL BOUNDS
2010
The tensorial Bernstein basis for multivariate polynomials in n variables has a number 3n of functions for degree 2. Consequently, computing the representation of a multivariate polynomial in the tensorial Bernstein basis is an exponential time algorithm, which makes tensorial Bernstein-based solvers impractical for systems with more than n = 6 or 7 variables. This article describes a polytope (Bernstein polytope) with a number of faces, which allows to bound a sparse, multivariate polynomial expressed in the canonical basis by solving several linear programming problems. We compare the performance of a subdivision solver using domain reductions by linear programming with a solver using a c…