9 papers
Multi-type -Wright--Fisher processes with polynomial drift: Bernstein duality, long-term behaviour, and simulation of moments
Sebastian Hummel
The -type -Wright--Fisher process with polynomial drift is a Lévy-type process on the -dimensional unit simplex whose generator entails a particular jump and diffusive…
Toric vector bundles and the number of zeros of vertical systems
Carles Checa
We provide necessary and sufficient conditions for the specializations of a vertically parametrized polynomial system to attain the maximal number of complex nonzero solutions. To…
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 hyperplan…
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…
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…
Solving bihomogeneous polynomial systems with a zero-dimensional projection
Matías 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
Matías 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…
Toric Sylvester forms
Laurent Busé, Carles Checa
In this paper, we investigate the structure of the saturation of ideals generated by sparse homogeneous polynomials over a projective toric variety with respect to the irreleva…
Mixed subdivisions suitable for the Canny-Emiris formula
Carles Checa, Ioannis Z. Emiris
The Canny-Emiris formula gives the sparse resultant as the ratio of the determinant of a Sylvester-type matrix over a minor of it, both obtained via a mixed subdivision algorithm.…