arXiv subjects

Andre Galligo

Publications and source records attributed to Andre Galligo.

2 recordsLinked to original sources

arXiv2003

A resultant approach to detect intersecting curves in $\PP^3$

Given two curves in $\PP^3$, either implicitly or by a parameterization, we want to check if they intersect. For that purpose, we present and further develop generalized resultant techniques. Our aim is to provide a closed formula in the inputs which vanishes if and only if the two curves intersect. This could be useful in Computer Aided Design, for computing the intersection of algebraic surfaces.

math.AG↗

arXiv1992

Grobner bases and extension of scalars

This paper studies the behavior of Grobner bases with respect to extensions of scalars. We prove that an extension of scalars commutes with taking Grobner bases iff the extension is flat. We consider what information can be deduced about fibers of a family, from the Grobner basis of the defining ideal of the family itself. This information can be used to construct algorithms, such as to find locii over which a map is finite, or an isomorphism.

alg-geom↗