23 citations · 57 across the 35 of their papers we have counts for
13 papers · 1 filter
Heights of complete intersections in toric varieties
Roberto Gualdi, Martín Sombra
The height of a toric variety and that of its hypersurfaces can be expressed in convex-analytic terms as an adelic sum of mixed integrals of their roof functions and duals of their…
The geometry of the flex locus of a hypersurface
Laurent Busé, Carlos D'Andrea, Martin Sombra +1
We give a formula in terms of multidimensional resultants for an equation for the flex locus of a projective hypersurface, generalizing a classical result of Salmon for surfaces. U…
Polynomial partitioning on varieties of codimension two and point-hypersurface incidences in four dimensions
Saugata Basu, Martin Sombra
We present a polynomial partitioning theorem for finite sets of points in the real locus of an irreducible complex algebraic variety of codimension at most two. This result general…
A Poisson formula for the sparse resultant
Carlos D'Andrea, Martin Sombra
We present a Poisson formula for sparse resultants and a formula for the product of the roots of a family of Laurent polynomials, which are valid for arbitrary families of supports…
Overdetermined systems of sparse polynomial equations
Francesco Amoroso, Louis Leroux, Martin Sombra
We show that, for a system of univariate polynomials given in sparse encoding, we can compute a single polynomial defining the same zero set, in time quasi-linear in the logarithm…
Arithmetic positivity on toric varieties
Jose Ignacio Burgos Gil, Atsushi Moriwaki, Patrice Philippon +1
We continue with our study of the arithmetic geometry of toric varieties. In this text, we study the positivity properties of metrized R-divisors in the toric setting. For a toric…