共查询到20条相似文献,搜索用时 15 毫秒
1.
A. M. Shermenev 《Mathematical Notes》1969,5(2):97-99
Nonsingular cubic surfaces in P3 and nonsingular intersections of two quadrics in P4 are investigated. It is proved that if a k-point exists on a surface, there is a k-point not on a line; k is the field over which the surfaces are defined.Translated from Matematicheskie Zametki, Vol. 5, No. 2, pp. 155–159, February, 1969.The author expresses his gratitude to Yu. I. Manin, under whose direction this work has been written. 相似文献
2.
We classify normal supersingular K 3 surfaces Y with total Milnor number 20 in characteristic p,where p is an odd prime that does not divide the discriminant of the Dynkin type of the rational double points on Y.This paper appeared in preprint form in the home page of the first author in the year 2005. 相似文献
3.
4.
5.
Tetsuji Shioda 《Mathematische Annalen》1977,225(2):155-159
6.
G. V. Ravindra 《Proceedings Mathematical Sciences》2006,116(1):37-50
Letk be a field of arbitrary characteristic. LetS be a singular surface defined overk with multiple rational curve singularities and suppose that the Chow group of zero cycles of its normalisation
is finite dimensional. We give numerical conditions under which the Chow group of zero cycles ofS is finite dimensional. 相似文献
7.
8.
9.
Mitsuru Kawazoe 《Journal of Pure and Applied Algebra》2006,204(3):602-615
Elliptic surfaces over an algebraically closed field in characteristic p>0 with multiple supersingular elliptic fibers, that is, multiple fibers of a supersingular elliptic curve, are investigated. In particular, it is shown that for an elliptic surface with q=g+1 and a supersingular elliptic curve as a general fiber, where q is the dimension of an Albanese variety of the surface and g is the genus of the base curve, the multiplicities of the multiple supersingular elliptic fibers are not divisible by p2. As an application of this result, the structure of false hyperelliptic surfaces is discussed on this basis. 相似文献
10.
11.
Stefan Schröer 《Arkiv f?r Matematik》2009,47(1):143-181
We study the geometry of Hilbert schemes of points on abelian surfaces and Beauville’s generalized Kummer varieties in positive
characteristics. The main result is that, in characteristic two, the addition map from the Hilbert scheme of two points to
the abelian surface is a quasifibration such that all fibers are nonsmooth. In particular, the corresponding generalized Kummer
surface is nonsmooth, and minimally elliptic singularities occur in the supersingular case. We unravel the structure of the
singularities in dependence of p-rank and a-number of the abelian surface. To do so, we establish a McKay Correspondence for Artin’s wild involutions on surfaces. Along
the line, we find examples of canonical singularities that are not rational singularities. 相似文献
12.
Andreas Schweizer 《manuscripta mathematica》2000,102(4):505-521
We show that extremal elliptic surfaces in characteristic 2 and 3 are unirational surfaces. Our strategy of proof is to determine explicit equations for the generic fibers. The method also applies to the classification of elliptic curves over k(T) with given places of bad reduction where k is any perfect field of characteristic 2 or 3. Received: 17 September 1999 / Revised version: 19 April 2000 相似文献
13.
This paper proposes a new geometric construction of Enriques surfaces. Its starting point are K3 surfaces with Jacobian elliptic fibration which arise from rational elliptic surfaces by a quadratic base change. The Enriques surfaces obtained in this way are characterised by elliptic fibrations with a rational curve as bisection which splits into two sections on the covering K3 surface. The construction has applications to the study of Enriques surfaces with specific automorphisms. It also allows us to answer a question of Beauville about Enriques surfaces whose Brauer groups show an exceptional behaviour. In a forthcoming paper, we will study arithmetic consequences of our construction. 相似文献
14.
Sungwook Lee 《Differential Geometry and its Applications》2008,26(5):536-543
A generalized integral representation formula for spacelike maximal surfaces in a certain 3-dimensional homogeneous spacetime is obtained. This spacetime has a solvable Lie group structure with left invariant metric. The normal Gauß map of maximal surfaces in the homogeneous spacetime is discussed and the harmonicity of the normal Gauß map is studied. 相似文献
15.
We prove that two derived equivalent twisted K3 surfaces have isomorphic periods. The converse is shown for K3 surfaces with large Picard number. It is also shown that all possible twisted derived equivalences between arbitrary twisted K3 surfaces form a subgroup of the group of all orthogonal transformations of the cohomology of a K3 surface.The passage from twisted derived equivalences to an action on the cohomology is made possible by twisted Chern characters that will be introduced for arbitrary smooth projective varieties. 相似文献
16.
Let X be a K3 surface over a number field K. We prove that there exists a finite algebraic field extension E/K such that X has ordinary reduction at every non-archimedean place of E outside a density zero set of places.
相似文献
17.
Mathematische Zeitschrift - We analyze morphisms from pointed curves to K3 surfaces with a distinguished rational curve, such that the marked points are taken to the rational curve, perhaps with... 相似文献
18.
19.
Francisco Javier Gallego B. P. Purnaprajna 《Transactions of the American Mathematical Society》1997,349(6):2477-2492
The purpose of this article is to study a certain kind of numerical K3 surfaces, the so-called K3 carpets. These are double structures on rational normal scrolls with trivial dualizing sheaf and irregularity . As is deduced from our study, K3 carpets can be obtained as degenerations of smooth K3 surfaces. We also study the Hilbert scheme near the locus parametrizing K3 carpets, characterizing those K3 carpets whose corresponding Hilbert point is smooth. Contrary to the case of canonical ribbons, not all K3 carpets are smooth points of the Hilbert scheme.
20.