We prove a closed formula for the integrals of the top Segre classes of tautological bundles over the Hilbert schemes of points of a K3 surface X. We derive relations among the Segre classes via equivariant localization of the virtual fundamental classes of Quot schemes on X. The resulting recursions are then solved explicitly. The formula proves the K-trivial case of a conjecture of M. Lehn fr...

In this note we compare two notions of Chern class of an algebraic scheme X (over C) specializing to the Chern class of the tangent bundle c(TX) ∩ [X] when X is nonsingular. The first of such notions is MacPherson’s Chern class, defined by means of Mather-Chern classes and local Euler obstructions [5]. MacPherson’s Chern class is functorial with respect to a push-forward defined via topological...

Recent developments in string theory suggest that there might exist extra spatial dimensions, which are not small nor compact. The framework of a great number of brane cosmological models is that in which the matter fields are confined on a brane-world embedded in five dimensions (the bulk). Motivated by this we review the main results on the algebraic classification of second order symmetric t...

In this paper, we will show that a vanishing generalized concurrence of a separable state can be seen as an algebraic variety called the Segre variety. This variety define a quadric space which gives a geometric picture of separable states. For pure, biand three-partite states the variety equals the generalized concurrence. Moreover, we generalize the Segre variety to a general multipartite sta...

1 Veronese rings, Segre embeddings or more generally Segre-Veronese embeddings are very important rings in Algebraic Geometry. In this paper we present an original, elementary way to compute the Hilbert-Poincare series of these rings, as a consequence we compute their Castelnuovo-Mumford regularity, and also the leading term of the h−vector. Moreover, we can compute the Castelnuovo-Mumford regu...

We show that the log canonical bundle, κ, of M0,n is very ample, show the homogeneous coordinate ring is Koszul, and give a nice set of rank 4 quadratic generators for the homogeneous ideal: The embedding is equivariant for the symmetric group, and the image lies on many Segre embedded copies of P×· · ·×P, permuted by the symmetric group. The homogeneous ideal of M0,n is the sum of the homogene...

Each embedded product space PG(n, q)×PG(n, q) in an (n2 +n− 1)-dimensional projective space is obtained by projecting the Segre variety Sn,n,q from an n-subspace δ skew with its first secant variety. On the other hand, when δ is skew with the (n − 1)-th secant variety, it determines a semifield of order qn+1 whose center contains Fq. A relationship arises between a particular class of embedding...

We study the Spohn conditional independence (CI) variety CX of an n-player game X for undirected graphical models on n binary random variables consisting one edge. For a generic game, we show that is smooth irreducible complete intersection curve (Nash curve) in Segre (P1)n−2×P3 and give explicit formula its degree genus. prove two universality theorems CX: The product any affine real algebraic...