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1.
We extend to normal projective varieties defined over an arbitrary algebraically closed field a result of Ein, Lazarsfeld, Musta??, Nakamaye and Popa characterizing the augmented base locus (aka non-ample locus) of a line bundle on a smooth projective complex variety as the union of subvarieties on which the restricted volume vanishes. We also give a proof of the folklore fact that the complement of the augmented base locus is the largest open subset on which the Kodaira map defined by large and divisible multiples of the line bundle is an isomorphism. 相似文献
2.
T. Nakano 《Transactions of the American Mathematical Society》1998,350(7):2903-2924
The birational geometry of projective threefolds on which acts with 2-dimensional general orbits is studied from the viewpoint of the minimal model theory of projective threefolds. These threefolds are closely related to the minimal rational threefolds classified by Enriques, Fano and Umemura. The main results are (i) the -birational classification of such threefolds and (ii) the classification of relatively minimal models in the fixed point free cases.
3.
《代数通讯》2013,41(6):1785-1794
ABSTRACT For projective codimension two surfaces and threefolds whose singular locus is one dimensional, we get the sharp Castelnuovo–Mumford regularity bound in terms of degrees of defining equations and give the classification of nearly extremal cases. This is a generalization of the result of Bertram et al. 相似文献
4.
Yoshinori Gongyo Zhiyuan Li Zsolt Patakfalvi Karl Schwede Hiromu Tanaka Runhong Zong 《Advances in Mathematics》2015
In this paper, we show that projective globally F -regular threefolds, defined over an algebraically closed field of characteristic p≥11, are rationally chain connected. 相似文献
5.
6.
Under suitable hypotheses, we prove that a form of a projective homogeneous variety G/P defined over the function field of a surface over an algebraically closed field has a rational point. The method uses an
algebro-geometric analogue of simple connectedness replacing the unit interval by the projective line. As a consequence, we
complete the proof of Serre’s Conjecture II in Galois cohomology for function fields over an algebraically closed field. 相似文献
7.
We describe birational models and decide the rationality/unirationality of moduli spaces A
d
(and A
d
lev
) of (1, d)-polarized Abelian surfaces (with canonical level structure, respectively) for small values of d. The projective lines identified in the rational/unirational moduli spaces correspond to pencils of Abelian surfaces traced on nodal threefolds living naturally in the corresponding ambient projective spaces, and whose small resolutions are new Calabi–Yau threefolds with Euler characteristic zero. 相似文献
8.
R. Barlow 《manuscripta mathematica》1996,90(1):155-174
A new criterion for rational equivalence of cycles on a projective variety over an algebraically closed field is given, and
some consequences considered. 相似文献
9.
Michał Kapustka 《manuscripta mathematica》2009,130(1):121-135
We describe two ways to construct finite rational morphisms between fiber products of rational elliptic surfaces with section
and some Calabi–Yau varieties. We use them to construct correspondences between such fiber products that admit at most five
singular fibers and rigid Calabi–Yau threefolds. 相似文献
10.
We prove that for smooth surfaces over real closed fields, and a class of smooth projective surfaces over a real number field, the map between mod 2 algebraic and étale K-theory is an isomorphism in sufficiently large degrees. For a class of smooth projective surfaces over a real closed field, including rational surfaces, complete intersections and K3-surfaces over the real numbers, we explicate the abutment of the mod 2 motivic cohomology to algebraic K-theory spectral sequence. 相似文献
11.
We give a universal approach to the deformation-obstruction theory of objects of the derived category of coherent sheaves
over a smooth projective family. We recover and generalise the obstruction class of Lowen and Lieblich, and prove that it
is a product of Atiyah and Kodaira–Spencer classes. This allows us to obtain deformation-invariant virtual cycles on moduli
spaces of objects of the derived category on threefolds. 相似文献
12.
Summary In this article we exhibit certain projective degenerations of smoothK3 surfaces of degree 2g–2 in
g
(whose Picard group is generated by the hyperplane class), to a union of two rational normal scrolls, and also to a union of planes. As a consequence we prove that the general hyperplane section of suchK3 surfaces has a corank one Gaussian map, ifg=11 org13. We also prove that the general such hyperplane section lies on a uniqueK3 surface, up to projectivities. Finally we present a new approach to the classification of prime Fano threefolds of index one, which does not rely on the existence of a line.Oblatum 1-II-1993 & 24-V-1993Research supported in part by NSF grant DMS-9104058 相似文献
13.
14.
Georg Hein 《Journal of Geometry》2004,79(1-2):89-101
We develop a formula (Theorem 5.2) which allows to compute top Chern classes of
vector bundles on the vanishing locus V(s) of a section of this bundle. This
formula particularly applies in the case when V(s) is the union of local complete
intersections giving the individual contribution of each component and their mutual
intersections. We conclude with applications to the enumeration of rational curves in
complete intersections in projective space. 相似文献
15.
Joseph W. Cutrone Nicholas A. Marshburn 《Central European Journal of Mathematics》2013,11(9):1552-1576
In this paper, examples of type II Sarkisov links between smooth complex projective Fano threefolds with Picard number one are provided. To show examples of these links, we study smooth weak Fano threefolds X with Picard number two and with a divisorial extremal ray. We assume that the pluri-anticanonical morphism of X contracts only a finite number of curves. The numerical classification of these particular smooth weak Fano threefolds is completed and the geometric existence of some numerical cases is proven. 相似文献
16.
G. Casnati 《Geometriae Dedicata》2006,119(1):169-179
We give a method for producing examples of Calabi–Yau threefolds as covers of degree d ≤ 8 of almost-Fano threefolds, computing explicitely their Euler– Poincaré characteristic. Such a method generalizes the well-knownclassical construction of Calabi–Yau threefolds as double covers of the projective space branched along octic surfaces. 相似文献
17.
Sijong Kwak 《Mathematische Annalen》2001,320(4):649-664
For a projective variety X of codimension 2 in defined over the complex number field , it is traditionally said that X has no apparent -ple points if the -secant lines of X do not fill up the ambient projective space , equivalently, the locus of -ple points of a generic projection of X to ${\Bbb P}^{n+1}$ is empty. We show that a smooth threefold in has no apparent triple points if and only if it is contained in a quadric hypersurface. We also obtain an enumerative formula
counting the quadrisecant lines of X passing through a general point of and give necessary cohomological conditions for smooth threefolds in without apparent quadruple points. This work is intended to generalize the work of F. Severi [fSe] and A. Aure [Au], where
it was shown that a smooth surface in has no triple points if and only if it is either a quintic elliptic scroll or contained in a hyperquadric. Furthermore we
give open questions along these lines.
Received: 24 January 2000 / Published online: 18 June 2001 相似文献
18.
Every complex projective space of odd dimension carries a natural contact structure. We give first steps towards the enumeration
of curves in ℙ3 tangent to the contact structure. Such a curve is involutive in the sense that its homogeneous ideal is closed under Poisson
bracket. Involutive curves in ℙ3 contained in a plane split as a union of concurrent lines. We give a formula for the number of plane involutive curves of
a given degree in ℙ3 meeting the appropriate number of lines. We also discuss strategies to deal with the enumeration of involutive rational curves. 相似文献
19.
Peter Vermeire 《Journal of Pure and Applied Algebra》2007,211(3):622-632
We compute the expected dimension of the moduli space of torsion-free rank 2 sheaves at a point corresponding to a stable reflexive sheaf, and give conditions for the existence of a perfect tangent-obstruction complex on a class of smooth projective threefolds; this class includes Fano and Calabi-Yau threefolds. We also explore both local and global relationships between moduli spaces of reflexive rank 2 sheaves and the Hilbert scheme of curves. 相似文献
20.
A. G. Kuznetsov 《Proceedings of the Steklov Institute of Mathematics》2009,264(1):110-122
We consider the structure of the derived categories of coherent sheaves on Fano threefolds with Picard number 1 and describe
a strange relation between derived categories of different threefolds. In the appendix we discuss how the ring of algebraic
cycles of a smooth projective variety is related to the Grothendieck group of its derived category.
Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2009, Vol. 264, pp. 116–128.
In memory of V.A. Iskovskikh 相似文献