共查询到20条相似文献,搜索用时 31 毫秒
1.
Angel Carocca Herbert Lange Rubí E. Rodríguez Anita M. Rojas 《Geometriae Dedicata》2009,139(1):219-231
Let X
1, ..., X
m
denote smooth projective curves of genus g
i
≥ 2 over an algebraically closed field of characteristic 0 and let n denote any integer at least equal to . We show that the product JX
1 × ... × JX
m
of the corresponding Jacobian varieties admits the structure of a Prym-Tyurin variety of exponent n
m-1. This exponent is considerably smaller than the exponent of the structure of a Prym-Tyurin variety known to exist for an
arbitrary principally polarized abelian variety. Moreover it is given by explicit correspondences.
相似文献
2.
We use properties of small resolutions of the ordinary double point in dimension three to construct smooth non-liftable Calabi-Yau
threefolds. In particular, we construct a smooth projective Calabi-Yau threefold over
\mathbbF3{\mathbb{F}_3} that does not lift to characteristic zero and a smooth projective Calabi-Yau threefold over
\mathbbF5{\mathbb{F}_5} having an obstructed deformation. We also construct many examples of smooth Calabi-Yau algebraic spaces over
\mathbbFp{\mathbb{F}_p} that do not lift to algebraic spaces in characteristic zero. 相似文献
3.
Serge Lvovski 《代数通讯》2013,41(12):4278-4280
In a recent article, Paltin Ionescu and Flavia Repetto proved that if X ? ? n is a smooth projective variety over ? such that its normal bundle sequence splits over some curve C ? X, then X a linear subspace in ? n . In this note, we give a purely geometric proof of this result that is valid in arbitrary characteristic. 相似文献
4.
Ji-hong SU & Yi-cai ZHAO LMAM Department of Mathematics Jinan University Guangzhou China 《中国科学A辑(英文版)》2007,50(4):495-502
Let X be a smooth projective variety of dimension 2k-1 (k≥3) over the complex number field. Assume that fR: X→Y is a small contraction such that every irreducible component Ei of the exceptional locus of fR is a smooth subvariety of dimension k. It is shown that each Ei is isomorphic to the k-dimensional projective space Pk, the k-dimensional hyperquadric surface Qk in Pk 1, or a linear Pk-1-bundle over a smooth curve. 相似文献
5.
6.
We prove a version of an effective Frobenius restriction theorem for semistable bundles in characteristic p. The main novelty is in restricting the bundle to the p-fold thickening of a hypersurface section. The base variety is G/P, an abelian variety or a smooth projective toric variety. 相似文献
7.
Marco Andreatta 《manuscripta mathematica》2003,110(4):505-512
We consider some conditions under which a smooth projective variety X is actually the projective space. We also extend to the case of positive characteristic some results in the theory of vector
bundle adjunction. We use methods and techniques of the so called Mori theory, in particular the study of rational curves
on projective manifolds.
Received: 16 May 2002 / Revised version: 18 November 2002 Published online: 3 March 2003
Mathematics Subject Classification (2000): 14E30, 14J40, 14J45 相似文献
8.
Mark E. Walker 《K-Theory》2000,21(2):101-140
We establish the existence of Adams operations on the members of a filtration of K-theory which is defined using products of projective lines. We also show that this filtration induces the gamma filtration on the rational K-groups of a smooth variety over a field of characteristic zero. 相似文献
9.
N. V. Timofeeva 《Mathematical Notes》2000,67(2):223-232
A. S. Tikhomirov’s conjecture about the smoothness of the variety of complete pairsX
23 of zero-dimensional subschemes of an irreducible projective algebraic surface is verified. In the caseS=P2, the topological Euler characteristic of this variety is computed.
Translated fromMatematicheskie Zametki, Vol. 67, No. 2, pp. 276–287, February, 2000. 相似文献
10.
Alexander Kemer 《Algebras and Representation Theory》2001,4(1):87-104
We describe the multilinear components of the prime subvarieties of the variety Var(M
2(F)) generated by the matrix algebra of order 2 over a field of characteristic p>0. 相似文献
11.
Burkhard Haastert 《manuscripta mathematica》1987,58(4):385-415
This paper is about differential operators andD-modules on a smooth variety over a field of positive characteristic. Beside some generalities the main results are theD-affinity of the projective space, theD-quasi-affinity of the ordinary flag manifolds (G/B) and theD-affinity of the ordinary flag manifold of Sl3. In contrast to characteristic 0 generally there exists some non-vanishing higher cohomology group of the associated graded algebra gr(D) on an ordinary flag manifold. 相似文献
12.
It is known that if a projective variety X in P
N
is reflexive with respect to the projective dual, then the Gauss map of X defined by embedded tangent spaces is separable, and moreover that the converse is not true in general. We prove that the
converse holds under the assumption that X is of dimension two. Explaining the subtleness of the problem, we present an example of smooth projective surfaces in arbitrary
positive characteristic, which gives a negative answer to a question raised by S. Kleiman and R. Piene on the inseparability
of the Gauss map.
相似文献
13.
Mohammed Abouzaid 《Selecta Mathematica, New Series》2009,15(2):189-270
Given a smooth projective toric variety X, we construct an A∞ category of Lagrangians with boundary on a level set of the Landau–Ginzburg mirror of X. We prove that this category is quasi-equivalent to the DG category of line bundles on X.
相似文献
14.
We study the relationship between the generic smoothness of the Gauss map and the reflexivity (with respect to the projective dual) for a projective variety defined over an algebraically closed field. The problem we discuss here is whether it is possible for a projective variety X in ℙN to re‐embed into some projective space ℙM so as to be non‐reflexive with generically smooth Gauss map. Our result is that the answer is affirmative under the assumption that X has dimension at least 3 and the differential of the Gauss map of X in ℙN is identically zero; hence the projective varietyX re‐embedded in ℙM yields a negative answer to Kleiman–Piene's question: Does the generic smoothness of the Gauss map imply reflexivity for a projective variety? A Fermat hypersurface in ℙN with suitable degree in positive characteristic is known to satisfy the assumption above. We give some new, other examples of X in ℙN satisfying the assumption. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
15.
We prove that any smooth complex projective variety X with plurigenera P
1(X)=P
2(X)=1 and irregularity q(X)=dim(X) is birational to an abelian variety.
Oblatum 26-V-1999 & 13-VI-2000?Published online: 11 October 2000 相似文献
16.
Norbert Hoffmann 《Central European Journal of Mathematics》2012,10(4):1306-1313
Let C be a smooth projective curve over an algebraically closed field of arbitrary characteristic. Let M r,L ss denote the projective coarse moduli scheme of semistable rank r vector bundles over C with fixed determinant L. We prove Pic(M r,L ss) = ℤ, identify the ample generator, and deduce that M r,L ss is locally factorial. In characteristic zero, this has already been proved by Drézet and Narasimhan. The main point of the present note is to circumvent the usual problems with Geometric Invariant Theory in positive characteristic. 相似文献
17.
Hajime Kaji 《Geometriae Dedicata》2009,139(1):75-82
In projective algebraic geometry, various pathological phenomena in positive characteristic have been observed by several authors. Many of those phenomena concerning the behavior of embedded tangent spaces seem to be controlled by the separability of (the extension of function fields defined by) the Gauss map, or by the reflexivity with respect to the projective dual for a projective variety. The purpose of this paper is to survey the studies on the relationship between the separability of the Gauss map and the reflexivity for a projective variety: Is the separability of the Gauss map equivalent to the reflexivity for a projective variety? 相似文献
18.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1997,324(12):1381-1384
We show that any hyperplane section of a variety which is the inverse image of a smooth variety of dimension at least 2 by an endomorphism (which is not an automorphism) of the projective space, is linearly complete. We stress the case of smooth surfaces in P4. 相似文献
19.
Boris Pasquier 《Mathematische Annalen》2009,344(4):963-987
We classify all smooth projective horospherical varieties with Picard number 1. We prove that the automorphism group of any
such variety X acts with at most two orbits and that this group still acts with only two orbits on X blown up at the closed orbit. We characterize all smooth projective two-orbit varieties with Picard number 1 that satisfy
this latter property. 相似文献
20.
Adrian Vasiu 《Mathematische Nachrichten》2020,293(12):2399-2448
We prove the existence of good smooth integral models of Shimura varieties of Hodge type in arbitrary unramified mixed characteristic (0, p). As a first application we provide a smooth solution (answer) to a conjecture (question) of Langlands for Shimura varieties of Hodge type. As a second application we prove the existence in arbitrary unramified mixed characteristic (0, p) of integral canonical models of projective Shimura varieties of Hodge type with respect to h-hyperspecial subgroups as pro-étale covers of Néron models; this forms progress towards the proof of conjectures of Milne and Reimann. Though the second application was known before in some cases, its proof is new and more of a principle. 相似文献