共查询到20条相似文献,搜索用时 187 毫秒
1.
Pierre-Emmanuel Chaput 《Mathematische Zeitschrift》2002,240(2):451-459
R. Hartshorne conjectured and F. Zak proved (cf [6,p.9]) that any smooth non-degenerate complex algebraic variety with satisfies denotes the secant variety of X; when X is smooth it is simply the union of all the secant and tangent lines to X). In this article, I deal with the limiting case of this theorem, namely the Severi varieties, defined by the conditions
and . I want to give a different proof of a theorem of F. Zak classifying all Severi varieties. F. Zak proves that there exists
only four Severi varieties and then realises a posteriori that all of them are homogeneous; here I will work in another direction:
I prove a priori that any Severi variety is homogeneous and then deduce more quickly their classification, satisfying R. Lazarsfeld
et A. Van de Ven's wish [6, p.18]. By the way, I give a very brief proof of the fact that the derivatives of the equation
of Sec(X), which is a cubic hypersurface, determine a birational morphism of . I wish to thank Laurent Manivel for helping me in writing this article.
Received in final form: 29 March 2001 / Published online: 1 February 2002 相似文献
2.
Johannes Huebschmann 《Differential Geometry and its Applications》2005,23(1):79-93
Each Scorza variety and its secant varieties in the ambient projective space are identified, in the realm of singular Poisson-Kähler geometry, in terms of projectivizations of holomorphic nilpotent orbits in suitable Lie algebras of hermitian type, the holomorphic nilpotent orbits, in turn, being affine varieties. The ambient projective space acquires an exotic Kähler structure, the closed stratum being the Scorza variety and the closures of the higher strata its secant varieties. In this fashion, the secant varieties become exotic projective varieties. In the rank 3 case, the four regular Scorza varieties coincide with the four critical Severi varieties. In the standard cases, the Scorza varieties and their secant varieties arise also via Kähler reduction. An interpretation in terms of constrained mechanical systems is included. 相似文献
3.
Jan Draisma 《Journal of Pure and Applied Algebra》2008,212(2):349-363
Tropical geometry yields good lower bounds, in terms of certain combinatorial-polyhedral optimisation problems, on the dimensions of secant varieties. The approach is especially successful for toric varieties such as Segre-Veronese embeddings. In particular, it gives an attractive pictorial proof of the theorem of Hirschowitz that all Veronese embeddings of the projective plane except for the quadratic one and the quartic one are non-defective; and indeed, no Segre-Veronese embeddings are known where the tropical lower bound does not give the correct dimension. Short self-contained introductions to secant varieties and the required tropical geometry are included. 相似文献
4.
Diane E. Davis 《Journal of Pure and Applied Algebra》2011,215(5):902-926
This paper is the second in a series leading to a type Bn geometric Littlewood-Richardson rule. The rule will give an interpretation of the Bn Littlewood-Richardson numbers as an intersection of two odd-orthogonal Schubert varieties and will consider a sequence of linear and quadratic deformations of the intersection into a union of odd-orthogonal Schubert varieties. This paper describes the setup for the rule and specifically addresses results for quadratic deformations, including a proof that at each quadratic degeneration, the results occur with multiplicity one. This work is strongly influenced by Vakil’s [14]. 相似文献
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7.
Nathan Owen Ilten 《Journal of Pure and Applied Algebra》2009,213(6):1086-1096
In the case of two-dimensional cyclic quotient singularities, we classify all one-parameter toric deformations in terms of certain Minkowski decompositions introduced by Altmann [Minkowski sums and homogeneous deformations of toric varieties, Tohoku Math. J. (2) 47 (2) (1995) 151-184.]. In particular, we show how to induce each deformation from a versal family, describe exactly to which reduced versal base space components each such deformation maps, describe the singularities in the general fibers, and construct the corresponding partial simultaneous resolutions. 相似文献
8.
Lety
2=x
3+a(t)x+b(t) be the equation of an elliptic curve over , wherea(t) andb(t) are polynomials over. We give an upper bound on average of the rank of such curves whent varies over under the assumption that theL-function attached to these curves satisfies classical assumptions. The proof is based on estimates of exponential sums, over varieties, which are treated by Deligne's theorem. 相似文献
9.
In this paper, we characterize those numerical semigroups containing 〈n1,n2〉. From this characterization, we give formulas for the genus and the Frobenius number of a numerical semigroup. These results can be used to give a method for computing the genus and the Frobenius number of a numerical semigroup with embedding dimension three in terms of its minimal system of generators. 相似文献
10.
M.H. Lim 《Linear and Multilinear Algebra》2013,61(3):231-234
In this note we give a simple proof and an extension of a dimension inequality of Howard concerning the range of a multilinear function with vector space range by using some results on algebraic varieties. 相似文献
11.
M.H. Lim 《Linear and Multilinear Algebra》2000,47(3):231-234
In this note we give a simple proof and an extension of a dimension inequality of Howard concerning the range of a multilinear function with vector space range by using some results on algebraic varieties. 相似文献
12.
In this paper we give a geometric characterization of the cones of toric varieties that are complete intersections. In particular,
we prove that the class of complete intersection cones is the smallest class of cones which is closed under direct sum and
contains all simplex cones. Further, we show that the number of the extreme rays of such a cone, which is less than or equal
to 2n − 2, is exactly 2n − 2 if and only if the cone is a bipyramidal cone, where n > 1 is the dimension of the cone. Finally, we characterize all toric varieties whose associated cones are complete intersection
cones.
Received: 4 July 2005 相似文献
13.
We give a new proof of the Jantzen sum formula for integral representations of Chevalley schemes over Spec Z, except for three exceptional cases. This is done by applying the fixed point formula of Lefschetz type in Arakelov geometry
to generalized flag varieties. Our proof involves the computation of the equivariant Ray-Singer torsion for all equivariant
bundles over complex homogeneous spaces. Furthermore, we find several explicit formulae for the global height of any generalized
flag variety.
Oblatum 17-VI-1999 & 10-IX-2001?Published online: 19 November 2001 相似文献
14.
Amaury Thuillier 《manuscripta mathematica》2007,123(4):381-451
V.G. Berkovich’s non-Archimedean analytic geometry provides a natural framework to understand the combinatorial aspects in
the theory of toric varieties and toroidal embeddings. This point of view leads to a conceptual and elementary proof of the
following results: if X is an algebraic scheme over a perfect field and if D is the exceptional normal crossing divisor of
a resolution of the singularities of X, the homotopy type of the incidence complex of D is an invariant of X. This is a generalization
of a theorem due to D. Stepanov. 相似文献
15.
We give an elementary proof, using nonstandard analysis, of the Jordan curve theorem. We also give a nonstandard generalization of the theorem. The proof is purely geometrical in character, without any use of topological concepts and is based on a discrete finite form of the Jordan theorem, whose proof is purely combinatorial.Some familiarity with nonstandard analysis is assumed. The rest of the paper is self-contained except for the proof a discrete standard form of the Jordan theorem. The proof is based on hyperfinite approximations to regions on the plane.Research of the first author partially supported by FONDECYT Grant # 91-1208 and of the second author, by FONDECYT Grant # 90-0647. 相似文献
16.
We prove the conjecture of Falikman-Friedland-Loewy on the parity of the degrees of projective varieties of n×n complex symmetric matrices of rank at most k. We also characterize the parity of the degrees of projective varieties of n×n complex skew symmetric matrices of rank at most 2p. We give recursive relations which determine the parity of the degrees of projective varieties of m×n complex matrices of rank at most k. In the case the degrees of these varieties are odd, we characterize the minimal dimensions of subspaces of n×n skew symmetric real matrices and of m×n real matrices containing a nonzero matrix of rank at most k. The parity questions studied here are also of combinatorial interest since they concern the parity of the number of plane partitions contained in a given box, on the one hand, and the parity of the number of symplectic tableaux of rectangular shape, on the other hand. 相似文献
17.
用构造性方法证明了以同一个特征向量为终端向量的Jordan链从始端向量到终端向量可以有不同的最大长度,并给出了Jordan基中Jordan链的某些性质,进一步完善了Jordan标准形过渡矩阵求法的补充条件. 相似文献
18.
用构造性方法证明了以同一个特征向量为终端向量的Jordan链从始端向量到终端向量可以有不同的最大长度,并给出了Jordan基中Jordan链的某些性质,进一步完善了Jordan标准形过渡矩阵求法的补充条件. 相似文献
19.
Izzet Coskun 《Advances in Mathematics》2011,(4):2441
This paper develops a new method for studying the cohomology of orthogonal flag varieties. Restriction varieties are subvarieties of orthogonal flag varieties defined by rank conditions with respect to (not necessarily isotropic) flags. They interpolate between Schubert varieties in orthogonal flag varieties and the restrictions of general Schubert varieties in ordinary flag varieties. We give a positive, geometric rule for calculating their cohomology classes, obtaining a branching rule for Schubert calculus for the inclusion of the orthogonal flag varieties in Type A flag varieties. Our rule, in addition to being an essential step in finding a Littlewood–Richardson rule, has applications to computing the moment polytopes of the inclusion of SO(n) in SU(n), the asymptotic of the restrictions of representations of SL(n) to SO(n) and the classes of the moduli spaces of rank two vector bundles with fixed odd determinant on hyperelliptic curves. Furthermore, for odd orthogonal flag varieties, we obtain an algorithm for expressing a Schubert cycle in terms of restrictions of Schubert cycles of Type A flag varieties, thereby giving a geometric (though not positive) algorithm for multiplying any two Schubert cycles. 相似文献
20.
Yoichi Mieda 《Advances in Mathematics》2010,225(4):2287-2297
In this article, we consider the representations of the general linear group over a non-archimedean local field obtained from the vanishing cycle cohomology of the Lubin-Tate tower. We give an easy and direct proof of the fact that no supercuspidal representation appears as a subquotient of such representations unless they are obtained from the cohomology of the middle degree. Our proof is purely local and does not require Shimura varieties. 相似文献