相关论文: Osculating spaces to secant varieties

We define many new examples of modules of equations for secant varieties of Segre varieties that generalize Strassen's commutation equations. Our modules of equations are obtained by constructing subspaces of matrices from tensors that…

In this paper we compute the dimension of all the higher secant varieties to the Segre-Veronese embedding of $\mathbb{P}^n\times \mathbb{P}^1$ via the section of the sheaf $\mathcal{O}(a,b)$ for any $n,a,b\in \mathbb{Z}^+$. We relate this…

Secant varieties are among the main protagonists in tensor decomposition, whose study involves both pure and applied mathematical areas. Grassmannians are the building blocks for skewsymmetric tensors. Although they are ubiquitous in the…

We present scheme theoretic methods that apply to the study of secant varieties. This mainly concerns finite schemes and their smoothability. The theory generalises to the base fields of any characteristic, and even to non-algebraically…

We prove a strong induction theorem for graded Hecke algebras and we classify the tempered and square integrable representations of such algebras using methods of equivariant homology.

We prove an analogue of Horrocks' splitting theorem for Segre-Veronese varieties building upon the theory of Tate resolutions on products of projective spaces.

We study the secant line variety of the Segre product of projective spaces using special cumulant coordinates adapted for secant varieties. We show that the secant variety is covered by open normal toric varieties. We prove that in cumulant…

We unify and generalize the notions of vacuum and amplitude in linear quantum field theory in curved spacetime. Crucially, the generalized notion admits a localization in spacetime regions and on hypersurfaces. The underlying concept is…

Using Morita type stratifications, we establish a one-to-one correspondence between geometric vector fields on a separated differentiable stack and stratified vector fields on its orbit space. This correspondence enables us to derive a…

In this paper, we study how simple linear projections of some projective varieties behave when the projection center runs through the ambient space. More precisely, let $X \subset \P^r$ be a projective variety satisfying Green-Lazarsfeld's…

In this paper we present a way of computing the degree of the secant (resp., tangent) variety of a smooth projective surface, under the assumption that the divisor giving the embedding in the projective space is $3$-very ample. This method…

We provide a characterization of homogeneous spaces under a reductive group scheme such that the geometric stabilizers are maximal tori. The quasi-split case over a semilocal base is of special interest and permits to answer a question…

We use a double degeneration technique to calculate the dimension of the secant variety of any Segre-Veronese embedding of (P^1)^r

We introduce and study the notion of orthosymmetric spaces over an Archimedean vector lattice as a generalization of finite-dimentional Euclidean inner spaces. A special attention has been paid to linear operators on these spaces.

Using supervector fields and graded forms along a morphism, we study the geometry of ordinary differential superequations, extend the formalism of higher order Lagrangian mechanics to the graded context and prove a generalization of…

In this short note we show that, for any ample embedding of a variety of dimension at least two in a projective space, all high enough degree Veronese re-embeddings have non-empty Terracini loci.

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,…

Given the space $V={\mathbb P}^{\binom{d+n-1}{n-1}-1}$ of forms of degree $d$ in $n$ variables, and given an integer $\ell>1$ and a partition $\lambda$ of $d=d_1+\cdots+d_r$, it is in general an open problem to obtain the dimensions of the…

This thesis is concerned with the application of operadic methods, particularly modular operads, to questions arising in the study of moduli spaces of surfaces as well as applications to the study of homotopy algebras and new constructions…

In the homotopical study of spaces of smooth embeddings, the functor calculus method (Goodwillie-Klein-Weiss manifold calculus) has opened up important connections to operad theory. Using this and a few simplifying observations, we arrive…