5 papers
Trivariate Splines on Fans of Hyperplane Arrangements and Koszul Homology
Carles Checa, Michael DiPasquale, Pablo Mazón +5
We study the space of splines where denotes a smoothness distribution and is the fan of a central hyperpl…
An effective criterion for multiple positive zeros of vertically parametrized polynomial systems
Carles Checa, Elisenda Feliu
We present an effective criterion for determining whether a (augmented) vertically parametrized polynomial system admits multiple positive zeros for some choice of parameter values…
A sparse overview on sparse resultants
Carles Checa, Ioannis Z. Emiris, Christos Konaxis
In this survey, we give an overview of advances in the theory and computation of sparse resultants. First, we examine the construction and proof of the Canny-Emiris formula, which…
Solving bihomogeneous polynomial systems with a zero-dimensional projection
MatÃas Bender, Laurent Busé, Carles Checa +1
We study bihomogeneous systems defining, non-zero dimensional, biprojective varieties for which the projection onto the first group of variables results in a finite set of points.…
Bigraded Castelnuovo-Mumford regularity and Gröbner bases
MatÃas Bender, Laurent Busé, Carles Checa +1
We study the relation between the bigraded Castelnuovo-Mumford regularity of a bihomogeneous ideal in the coordinate ring of the product of two projective spaces and the bidegr…