Related papers: Horrocks splitting on Segre-Veronese varieties

We prove a Horrocks-type splitting criterion for arbitrary smooth projective toric varieties under an additional hypothesis similar to the case of products of projective spaces by Eisenbud--Erman--Schreyer.

We generalize Horrocks' criterion for the splitting of vector bundles on projective space. We establish an analogous splitting criterion for vector bundles on a class of smooth complex projective varieties of dimension at least four, over…

We prove the rationality of a $\k$-form $X$ of the product $S$ of projective spaces provided the existence of a $\k$-point on $X$. The method of the proof is to find a Galois-invariant birational projection of $S$ to the projective space.…

We determine the minimal generators of the ideal of the tangential variety of a Segre-Veronese variety, as well as the decomposition into irreducible GL-representations of its homogeneous coordinate ring. In the special case of a Segre…

We prove that the ideal of the variety of secant lines to a Segre--Veronese variety is generated in degree three by minors of flattenings. In the special case of a Segre variety this was conjectured by Garcia, Stillman and Sturmfels,…

We give an explicit description of the terms and differentials of the Tate resolution of sheaves arising from Segre embeddings of $\P^a\times\P^b$. We prove that the maps in this Tate resolution are either coming from Sylvester-type maps,…

We prove (with a mild restriction on the multidegrees) that all secant varieties of Segre-Veronese varieties with $k>2$ factors, $k-2$ of them being $\mathbb{P}^1$, have the expected dimension. This is equivalent to compute the dimension of…

This paper explores the dimensions of higher secant varieties to Segre-Veronese varieties. The main goal of this paper is to introduce two different inductive techniques. These techniques enable one to reduce the computation of the…

By analogy with algebraic geometry, we define a category of non-linear sheaves (quasi-coherent homotopy-sheaves of topological spaces) on projective toric varieties and prove a splitting result for its algebraic K-theory, generalising…

Our main aim is to provide a uniform geometric characterization of the analogues over arbitrary fields of the four complex Severi varieties, i.e.~the quadric Veronese varieties in 5-dimensional projective spaces, the Segre varieties in…

We construct an explicit equivalence between a category of complexes over the exterior algebra, which we call HT-complexes, and the stable category of vector bundles on the corresponding projective space, and establish a relation between…

We classify morphisms from proper varieties to Brauer-Severi varieties, which generalizes the classical correspondence between morphisms to projective space and globally generated invertible sheaves. As an application, we study del Pezzo…

We determine set theoretic defining equations for the third secant variety of the Segre product of $n$ projective spaces, and from the proof of the main statement we derive an upper bound for the degrees of these equations.

We define new classes of modules of equations for secant varieties of Veronese varieties using representation theory and geometry. We also revisit some old modules of equations (catalecticant minors) to determine when they are sufficient to…

We establish an equivalence between the stable category of coherent sheaves (satisfying a mild restriction) on a projective space and the homotopy category of a certain class of minimal complexes of free modules over the exterior algebra…

We connect Veronese embeddings to splitting varieties of cup products. We then give an algorithm for constructing splitting varieties for cup products with $\mathbb Z/n$ coefficients, with an explicit calculation for $n=3$. An application…

We give an almost asymptotically sharp bound for the non secant defectiveness and identifiability of Segre-Veronese varieties. We also provide new examples of defective Segre-Veronese varieties.

We prove under some assumptions that the Tate conjecture holds for products of Fermat varieties of different degrees.

We give an algorithm for computing Segre classes of subschemes of arbitrary projective varieties by computing degrees of a sequence of linear projections. Based on the fact that Segre classes of projective varieties commute with…

We consider here the problem, which is quite classical in Algebraic geometry, of studying the secant varieties of a projective variety $X$. The case we concentrate on is when $X$ is a Veronese variety, a Grassmannian or a Segre variety. Not…