2 citations · 3 across the 5 of their papers we have counts for
8 papers
Diophantine geometry and toric varieties
Patrice Philippon, Martin Sombra
We present some results on projective toric varieties which are relevant in Diophantine geometry. We interpret and study several invariants attached to these varieties in geometric…
Normalized height of projective toric varieties
Patrice Philippon, Martin Sombra
We present an explicit expression for the normalized height of a projective toric variety. This expression decomposes as a sum of local contributions, each term being the integral…
The Cayley-Menger determinant is irreducible for
Carlos D'Andrea, Martin Sombra
We prove that the Cayley-Menger determinant of an -dimensional simplex is an absolutely irreducible polynomial for We also study the irreducibility of polynomials asso…
The height of the mixed sparse resultant
Martin Sombra
We present an upper bound for the height of the mixed sparse resultant, defined as the logarithm of the maximum modulus of its coefficients. We obtain a similar estimate for its Ma…
The computational complexity of the Chow form
Gabriela Jeronimo, Teresa Krick, Juan Sabia +1
We present a bounded probability algorithm for the computation of the Chow forms of the equidimensional components of an algebraic variety. Its complexity is polynomial in the leng…
Intrinsic palindromic numbers
Antonio J. Di Scala, Martin Sombra
We introduce a notion of palindromicity of a natural number which is independent of the base. We study the existence and density of palindromic and multiple palindromic numbers, an…