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1.
This paper is devoted to a problem of finding the smallest positive integer s(m,n,k)s(m,n,k) such that (m+1)(m+1) generic skew-symmetric (k+1)(k+1)-forms in (n+1)(n+1) variables as linear combinations of the same s(m,n,k)s(m,n,k) decomposable skew-symmetric (k+1)(k+1)-forms.  相似文献   

2.
Let X be a non-degenerate, not necessarily linearly normal projective variety in . Recently the generalization of property N p to non-linearly normal projective varieties have been considered and its algebraic and geometric properties are studied extensively. One of the generalizations is the property N d,p for the saturated ideal I X (Eisenbud et al. in Compos Math 141: 1460–1478, 2005) and the other is the property for the graded module of the twisted global sections of (Kwak and Park in J Reine Angew Math 582: 87–105, 2005). In this paper, we are interested in the algebraic and geometric meaning of properties for every p ≥ 0 and the syzygetic behaviors of isomorphic projections and hyperplane sections of a given variety with property . Youngook Choi and Sijong Kwak were supported in part by KRF (grant No. 2005-070-C00005).  相似文献   

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This paper concerns G-invariant systems of second-order differential operators on irreducible Hermitian symmetric spaces G/K. The systems of type (1,1) are obtained from K-invariant subspaces of . We show that all such systems can be derived from a decomposition . Here gives the Laplace-Beltrami operator and is the celebrated Hua system, which has been extensively studied elsewhere. Our main result asserts that for G/K of rank at least two, a bounded real-valued function is annihilated by the system if and only if it is the real part of a holomorphic function. In view of previous work, one obtains a complete characterization of the bounded functions that are solutions for any system of type (1,1) which contains the Laplace-Beltrami operator.  相似文献   

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In this note, we give a bound for the Castelnuovo-Mumford regularity of a homogeneous ideal I in terms of the degrees of its generators. We assume that I defines a local complete intersection with log canonical singularities.  相似文献   

7.
A compact complex manifold X obtained by taking quotient of a bounded symmetric domain has an ample canonical line bundle. We prove that the dimension of very ample pluricanonical subsystem is strictly bigger than 2n, where n is the dimension of X. Received: 23 June 2000 / Revised version: 30 March 2001  相似文献   

8.
Let V1, V2 and V3 be vector spaces over any field k. An element TV1V2V3 induces for each i=1,2,3 a k-linear map where is the dual vector space of Vi. We characterize all integer triplets (r1,r2,r3) such that there exists a tensor T with ri=rankTi, and we explain how these ranks are related to the higher secant varieties of various Segre varieties. We also study the case TV1⊗?⊗Vn with n>3, giving necessary conditions on the ranks of all induced linear maps.  相似文献   

9.
Inspired by results of Guardo, Van Tuyl and the second author for lines in P3P3, we develop asymptotic upper bounds for the least degree of a homogeneous form vanishing to order at least m on a union of disjoint r  -dimensional planes in PnPn for n?2r+1n?2r+1. These considerations lead to new conjectures that suggest that the well known conjecture of Nagata for points in P2P2 is not an exotic statement but rather a manifestation of a much more general phenomenon which seems to have been overlooked so far.  相似文献   

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This paper deals with syzygies of the ideals of Segre embeddings. Let d≥3 and . We prove that satisfies Green-Lazarsfeld’s property Np if and only if p≤3.  相似文献   

14.
Let X be a variety over a perfect field k and let X be its space of arcs. Given a closed subset Z of X, let XZ denote the subscheme of X consisting of all arcs centered at some point of Z. We prove that Local Uniformization implies that XZ has a finite number of irreducible components for each closed subset Z of X. In particular, Local Uniformization implies that XSingX has a finite number of irreducible components.  相似文献   

15.
We generalize the classical Terracini’s Lemma to higher order osculating spaces to secant varieties. As an application, we address with the so-called Horace method the case of thed-Veronese embedding of the projective 3-space. This research is part of the T.A.S.C.A. project of I.N.d.A.M., supported by P.A.T. (Trento) and M.I.U.R. (Italy).  相似文献   

16.
We construct new examples of exceptional collections of line bundles on the variety of Borel subgroups of a split semisimple linear algebraic group GG of rank 2 over a field. We exhibit exceptional collections of the expected length for types A2A2 and B2=C2B2=C2 and prove that no such collection exists for type G2G2. This settles the question of the existence of full exceptional collections of line bundles on projective homogeneous GG-varieties for split linear algebraic groups GG of rank at most 2.  相似文献   

17.
We prove a Hermitian metric rigidity theorem for leafwise symmetric Kaehler metrics on compact manifolds with smooth foliations. This provides applications to the study of the geometry of foliations as well as Kaehler manifolds that contain some symmetric geometry.  相似文献   

18.
The standard Poisson structure on the rectangular matrix variety Mm,n(C) is investigated, via the orbits of symplectic leaves under the action of the maximal torus TGLm+n(C). These orbits, finite in number, are shown to be smooth irreducible locally closed subvarieties of Mm,n(C), isomorphic to intersections of dual Schubert cells in the full flag variety of GLm+n(C). Three different presentations of the T-orbits of symplectic leaves in Mm,n(C) are obtained: (a) as pullbacks of Bruhat cells in GLm+n(C) under a particular map; (b) in terms of rank conditions on rectangular submatrices; and (c) as matrix products of sets similar to double Bruhat cells in GLm(C) and GLn(C). In presentation (a), the orbits of leaves are parametrized by a subset of the Weyl group Sm+n, such that inclusions of Zariski closures correspond to the Bruhat order. Presentation (b) allows explicit calculations of orbits. From presentation (c) it follows that, up to Zariski closure, each orbit of leaves is a matrix product of one orbit with a fixed column-echelon form and one with a fixed row-echelon form. Finally, decompositions of generalized double Bruhat cells in Mm,n(C) (with respect to pairs of partial permutation matrices) into unions of T-orbits of symplectic leaves are obtained.  相似文献   

19.
We prove a Fatou-type theorem on a homogeneous line bundle over a Hermitian symmetric space, and characterize the range of the Poisson transform of Lp -functions on the maximal boundary as a Hardy-type space.  相似文献   

20.
Let X be a smooth irreducible non-degenerated projective curve in some projective space PN. Let r be a positive integer such that 2r + 1 < N and let Sr(X) be the r-th secant variety of X. It is a variety of dimension 2r + 1. In this paper we prove that the singular locus is the (r - 1)-th secant variety Sr- 1(X) if X does not have any (2r + 2)-secant 2r-space divisor. Received: 26 November 2002  相似文献   

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