Monomial ideals and toric rings are closely related. By consider a Grobner basis we can always associated to any ideal I in a polynomial ring a monomial ideal in≺I, in some special situations the monomial ideal in≺I is square free. On the other hand given any monomial ideal I of a polynomial ring S, we can define the toric K[I] ⊂ S. In this paper we will study toric rings defined by Segre embed...

The notion of m-regular system on the Hermitian variety H(n, q2) was introduced by B. Segre (Ann. Math. Pura Appl. 70:1–201, 1965). Here, three infinite families of hemisystems on H(5, q2), q odd, are constructed.

We generalize a result of Segre on permutable orthogonal and unitary polarities of PG(2, q) with q odd, by considering non-desarguesian projective planes of odd square order.

We propose a Riemannian conjugate gradient algorithm for approximating incomplete tensors by canonical polyadic decompositions of low rank. Our main contribution consists an explicit expression almost everywhere complete set geodesics the Segre manifold rank-1 tensors. These are leveraged in our optimization over geometrically convenient parametrization rank- r $$ to move direction tangent vect...