共查询到20条相似文献,搜索用时 15 毫秒
1.
I. V. Netay 《Functional Analysis and Its Applications》2013,47(3):210-226
We describe the syzygy spaces for the Segre embedding ?(U) × ?(V) ? ?(U ? V) in terms of representations of GL(U) × GL(V) and construct the minimal resolutions of the sheaves (a, b) in D(?(U ? V)) for a ? ?dim(U) and b ? ?dim(V). We also prove a property of multiplication in syzygy spaces of the Segre embedding. 相似文献
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Nathan Grieve 《Geometriae Dedicata》2013,162(1):1-7
We prove that there is no g for which the canonical embedding of a general curve of genus g lies on the Segre embedding of any product of three or more projective spaces. 相似文献
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Elena Rubei 《Journal of Pure and Applied Algebra》2007,208(1):29-37
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
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Elena Rubei 《Transactions of the American Mathematical Society》2000,352(6):2569-2579
In this paper we prove the following result: Let be a complex torus and a normally generated line bundle on ; then, for every , the line bundle satisfies Property of Green-Lazarsfeld.
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Laurent Manivel 《Proceedings of the American Mathematical Society》1996,124(8):2293-2299
We show that on a complex flag manifold, a very ample line bundle which is a -th power has property in the sense of Green and Lazarsfeld. This is a partial answer to a problem raised by Fulton.
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Euisung Park 《Transactions of the American Mathematical Society》2006,358(8):3733-3749
We study higher syzygies of a ruled surface over a curve of genus with the numerical invariant . Let Pic be a line bundle in the numerical class of . We prove that for , satisfies property if and , and for , satisfies property if and . By using these facts, we obtain Mukai-type results. For ample line bundles , we show that satisfies property when and or when and . Therefore we prove Mukai's conjecture for ruled surface with . We also prove that when is an elliptic ruled surface with , satisfies property if and only if and .
9.
Hajime Kaji 《Geometriae Dedicata》2003,99(1):221-229
The reflexivity, the (semi-)ordinariness, the dimension of dual varieties and the structure of Gauss maps are discussed for Segre varieties, where a Segre variety is the image of the product of two or more projective spaces under Segre embedding. A generalization is given to a theorem of A. Hefez and A. Thorup on Segre varieties of two projective spaces. In particular, a new proof is given to a theorem of F. Knop, G. Menzel, I. M. Gelfand, M.M. Kapranov and A. V. Zelevinsky that states a necessary and sufficient condition for Segre varieties to have codimension one duals. On the other hand, a negative answer is given to a problem raised by S. Kleiman and R. Piene as follows: For a projective variety of dimension at least two, do the Gauss map and the natural projection from the conormal variety to the dual variety have the same inseparable degree? 相似文献
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Seshadri Chintapalli 《Journal of Pure and Applied Algebra》2019,223(6):2413-2424
Syzygies or -property of an ample line bundles on abelian varieties are well known. In this paper, we study defining equations and syzygies among them of projective bundles over abelian varieties. We prove an analogue of Pareschi's theorem (or Lazarsfeld's conjecture) on abelian varieties, extended to projective bundles over an abelian variety. 相似文献
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Euisung Park 《Mathematische Nachrichten》2014,287(11-12):1383-1393
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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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Enzo Martinelli 《Annali di Matematica Pura ed Applicata》1978,116(1):I-III
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Alexandru Dimca 《Annali dell'Universita di Ferrara》2017,63(1):87-101
We give lower bounds for the degree of the syzygies involving the partial derivatives of a homogeneous polynomial defining an even dimensional nodal hypersurface. This implies the validity of formulas due to M. Saito, L. Wotzlaw and the author for the graded pieces with respect to the Hodge filtration of the top cohomology of the hypersurface complement in many new cases. A classical result by Severi on the position of the singularities of a nodal surface in \(\mathbb {P}^3\) is improved and applications to deformation theory of nodal surfaces are given. 相似文献
20.
We establish basic techniques for determining the ideals of secant varieties
of Segre varieties.We solve a conjecture of Garcia, Stillman, and Sturmfels on
the generators of the ideal of the first secant variety in the case of three factors and
solve the conjecture set-theoretically for an arbitrary number of factors. We determine
the low degree components of the ideals of secant varieties of small dimension
in a few cases. 相似文献