共查询到20条相似文献,搜索用时 15 毫秒
1.
Pierre-Emmanuel Chaput 《Indagationes Mathematicae》2003,14(2):169-182
In this paper, I give two very direct proves of the correspondance between a geometric object (Scorza varieties) and an algebraic one (Jordan algebras). I also give a short proof of the homogeneity of Scorza varieties, and a new and very simple proof of properties of the automorphism group of a Jordan algebra. 相似文献
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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
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Let X be the blow-up of the three dimensional complex projective space along r points in very general position on a smooth elliptic quartic curve B⊂P3 and let L∈Pic(X) be any line bundle. The aim of this paper is to provide an explicit algorithm for determining the dimension of H0(X,L). 相似文献
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Dmitri Zaitsev 《Mathematische Annalen》1995,302(1):105-129
This paper is a part of author's doctoral thesis. It was partially supported by Sonderforschungsbereich 237 Unordnung und große Fluktuatuionen of the Deutsche Forschungsgemeinschaft 相似文献
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John Kopper 《Journal of Pure and Applied Algebra》2018,222(4):846-867
In this paper we study the pseudoeffective cones of blow-ups of Grassmannians at sets of points. For small numbers of points, the cones are often spanned by proper transforms of Schubert classes. In some special cases, we provide sharp bounds for when the Schubert classes fail to span and we describe the resulting geometry. 相似文献
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We study components and dimensions of higher-order determinantal varieties obtained by considering generic m×n (m?n) matrices over rings of the form F[t]/(tk), and for some fixed r, setting the coefficients of powers of t of all r×r minors to zero. These varieties can be interpreted as spaces of (k−1)th order jets over the classical determinantal varieties; a special case of these varieties first appeared in a problem in commuting matrices. We show that when r=m, the varieties are irreducible, but when r<m, these varieties are reducible. We show that when r=2<m (any k), there are exactly ⌊k/2⌋+1 components, which we determine explicitly, and for general r<m, we show there are at least ⌊k/2⌋+1 components. We also determine the components explicitly for k=2 and 3 for all values of r (for k=3 for all but finitely many pairs of (m,n)). 相似文献
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We introduce notions of combinatorial blowups, building sets, and
nested sets for arbitrary meet-semilattices. This gives a~common abstract
framework for the incidence combinatorics occurring in the context of
De Concini-Procesi models of subspace arrangements and resolutions
of singularities in toric varieties.
Our main theorem states that a sequence of combinatorial blowups,
prescribed by a building set in linear extension compatible order,
gives the face poset of the corresponding simplicial complex of nested sets.
As applications we trace the incidence combinatorics through every
step of the De Concini-Procesi model construction, and we introduce
the notions of building sets and nested sets to the context of toric
varieties.
There are several other instances, such as models of stratified
manifolds and certain graded algebras associated with finite lattices,
where our combinatorial framework has been put to work; we present
an outline at the end of this paper. 相似文献
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Aaron Reite 《Journal of Pure and Applied Algebra》2008,212(6):1367-1380
In this paper we define model solvmanifold pairs and their diagonal type selfmaps in the tradition of Heath and Keppelmann. We derive an explicit formula for computing the relative Nielsen number N(F;X,A) on these spaces and selfmaps F:(X,A)→(X,A). We find that model solvmanifold pairs often exhibit interesting Schirmer theory, meaning N(F;X,A)>max{N(F),N(F|A)}. 相似文献
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Mustapha Lahyane 《Journal of Pure and Applied Algebra》2010,214(7):1217-1240
We give a numerical criterion for ensuring the finite generation of the effective monoid of the surfaces obtained by a blowing-up of the projective plane at the supports of zero dimensional subschemes assuming that these are contained in a degenerate cubic. Furthermore, this criterion also ensures the regularity of any numerically effective divisor on these surfaces. Thus the dimension of any complete linear system is computed. On the other hand, in particular and among these surfaces, we obtain ringed rational surfaces with very large Picard numbers and with only finitely many integral curves of strictly negative self-intersection. These negative integral curves except two (−1)-curves are all contained in the support of an anticanonical divisor. Thus almost all the geometry of such surfaces is concentrated in the anticanonical class. 相似文献
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《Mathematische Nachrichten》2018,291(8-9):1374-1389
We prove that if X is a rationally connected threefold and G is a p‐subgroup in the group of birational selfmaps of X, then G is an abelian group generated by at most 3 elements provided that . We also prove a similar result for under an assumption that G acts on a (Gorenstein) G‐Fano threefold, and show that the same holds for under an assumption that G acts on a G‐Mori fiber space. 相似文献
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《Quaestiones Mathematicae》2013,36(7):939-951
AbstractIn this paper, connectedness is completely characterized for the complements of the zero-divisor graphs of partially ordered sets. These results are applied to annihilating ideal graphs and intersection graphs of submodules, generalizing some of the work that has recently appeared in the literature. 相似文献
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We compute the Chow motive of certain subvarieties of the Flags manifold and show that it is an Artin motive. 相似文献
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Cindy De Volder 《Monatshefte für Mathematik》2004,143(1):61-80
We consider a rational surface Xr, obtained by blowing up 2 along a curvilinear zero-dimensional subscheme of length r of the regular locus of a reduced irreducible plane curve of degree d, with d 4; and we give sufficient conditions for d-standard classes to be very ample (resp. base point free or non special) on such a rational surface Xr.Postdoctoral Fellow of the Fund for Scientific Research-Flanders (Belgium). 相似文献
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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
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Joaquín Moraga 《Journal of Pure and Applied Algebra》2019,223(8):3225-3237
In this note, we study linear systems on complete toric varieties X with an invariant point whose orbit under the action of contains the dense torus T of X. We give a characterization of such varieties in terms of its defining fan and introduce a new definition of expected dimension of linear systems which consider the contribution given by certain toric subvarieties. Finally, we study degenerations of linear systems on these toric varieties induced by toric degenerations. 相似文献