共查询到20条相似文献,搜索用时 15 毫秒
1.
We study a Seshadri constant at a general point on a rational surface whose anticanonical linear system contains a pencil. First, we describe a Seshadri constant of an ample line bundle on such a rational surface explicitly by the numerical data of the ample line bundle. Second, we classify log del Pezzo surfaces which are special in terms of the Seshadri constants of the anticanonical divisors when the anticanonical degree is between 4 and 9. 相似文献
2.
Stefan Schröer 《Mathematische Annalen》2001,321(2):439-454
Using Maruyama's theory of elementary transformations, I show that the Brauer group surjects onto the cohomological Brauer
group for separated geometrically normal algebraic surfaces. As an application, I infer the existence of nonfree vector bundles
on proper normal algebraic surfaces.
Received: 14 April 2000 / Accepted: 26 February 2001 / Published online: 23 July 2001 相似文献
3.
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
4.
Stefan Schröer 《manuscripta mathematica》1999,100(3):317-321
In this note we construct examples of non-projective normal proper algebraic surfaces and discuss the somewhat pathological behaviour of their Neron–Severi group. Our surfaces
are birational to the product of a projective line and a curve of higher genus.
Received: 29 January 1999 相似文献
5.
In this paper we investigate the relation between the finite generation of the Cox ring R(X) of a smooth projective surface X and its anticanonical Iitaka dimension κ(−KX). 相似文献
6.
We show that any Fano fivefold with canonical Gorenstein singularities has an effective anticanonical divisor. Moreover, if a general element of the anticanonical system is reduced, then it has canonical singularities. 相似文献
7.
H. Kojima 《Archiv der Mathematik》2001,77(6):517-521
We study normal complete algebraic surfaces with strictly nef anticanonical divisors defined over an algebraically closed field of arbitrary characteristic. We prove that such surfaces have numerically ample anticanonical divisors. 相似文献
8.
Ravi Vakil 《manuscripta mathematica》2000,102(1):53-84
In [CH3], Caporaso and Harris derive recursive formulas counting nodal plane curves of degree d and geometric genus g in the plane (through the appropriate number of fixed general points). We rephrase their arguments in the language of maps,
and extend them to other rational surfaces, and other specified intersections with a divisor. As applications, (i) we count
irreducible curves on Hirzebruch surfaces in a fixed divisor class and of fixed geometric genus, (ii) we compute the higher-genus
Gromov–Witten invariants of (or equivalently, counting curves of any genus and divisor class on) del Pezzo surfaces of degree
at least 3. In the case of the cubic surface in (ii), we first use a result of Graber to enumeratively interpret higher-genus
Gromov–Witten invariants of certain K-nef surfaces, and then apply this to a degeneration of a cubic surface.
Received: 30 June 1999 / Revised version: 1 January 2000 相似文献
9.
D. Markushevich 《Mathematische Annalen》2008,342(1):145-156
Given a K3 surface S, we show that the relative intermediate Jacobian of the universal family of Fano 3-folds V containing S as an anticanonical divisor is a Lagrangian fibration. 相似文献
10.
We construct families of normal surface singularities with the following property: given any fiat projective connected family V →B of smooth, irreducible, minimal algebraic surfaces, the general singularity in one of our families cannot occur, analytically, on any algebraic surfaces which is Irrationally equivalent to a surface in V→B. In particular this holds for V→B consisting of a single rational surface, thus answering negatively to a long standing problem posed by F. Enriques. In order to prove the above mentioned results, wo develop a general, though elementary, method, based on the consideration of suitable correspondences, for comparing a given family of minimal surfaces with a family of surface singularities. Specifically the method in question gives us the possibility of comparing the parameters on which the two families depend, thus leading to the aforementioned results. 相似文献
11.
Amaël Broustet 《Mathematische Annalen》2009,343(4):727-755
We show how to use effective non-vanishing to prove that Seshadri constants of some ample divisors are bigger than 1 on smooth
threefolds whose anticanonical bundle is nef or on Fano varieties of small coindice. We prove the effective non-vanishing
conjecture of Ionescu–Kawamata in dimension 3 in the case of line bundles of “high” volume. 相似文献
12.
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
13.
Stable surfaces and their log analogues are the type of varieties naturally occurring as boundary points in moduli spaces. We extend classical results of Kodaira and Bombieri to this more general setting: if (X,Δ) is a stable log surface with reduced boundary (possibly empty) and I is its global index, then 4I(KX+Δ) is base-point-free and 8I(KX+Δ) is very ample. 相似文献
14.
We study the behavior of the Yang-Mills flow for unitary connections on compact and non-compact oriented surfaces with varying
metrics. The flow can be used to define a one dimensional foliation on the space of representations of a once punctured surface. This foliation universalizes over Teichmüller space and is equivariant with
respect to the action of the mapping class group. It is shown how to extend the foliation as a singular foliation over the
augmented boundary of Teichmüller space obtained by adding nodal Riemann surfaces. Continuity of this extension is the main
result of the paper.
Received May 18, 1998 / Revised August 30, 1999 / Published online July 20, 2000 相似文献
15.
In [L. Chiantini, T. Markwig, Triple-point defective regular surfaces. arXiv:0705.3912, 2007] we studied triple-point defective very ample linear systems on regular surfaces, and we showed that they can only exist if the surface is ruled. In the present paper we show that we can drop the regularity assumption, and we classify the triple-point defective very ample linear systems on ruled surfaces. 相似文献
16.
In this note, we study the action of finite groups of symplectic automorphisms on K3 surfaces which yield quotients birational
to generalized Kummer surfaces. For each possible group, we determine the Picard number of the K3 surface admitting such an
action and for singular K3 surfaces we show the uniqueness of the associated abelian surface.
Received: 9 April 1998 / Revised version: 17 July 1998 相似文献
17.
The main goal of this paper is to give a general algorithm to compute, via computer-algebra systems, an explicit set of generators of the ideals of the projective embeddings of ruled surfaces, i.e. projectivizations of rank two vector bundles over curves, such that the fibers are embedded as smooth rational curves.There are two different applications of our algorithm. Firstly, given a very ample linear system on an abstract ruled surface, our algorithm allows computing the ideal of the embedded surface, all the syzygies, and all the algebraic invariants which are computable from its ideal as, for instance, the k-regularity. Secondly, it is possible to prove the existence of new embeddings of ruled surfaces.The method can be implemented over any computer-algebra system able to deal with commutative algebra and Gröbner-basis computations. An implementation of our algorithms for the computer-algebra system Macaulay2 (cf. [Daniel R. Grayson, Michael E. Stillman, Macaulay 2, a software system for research in algebraic geometry, 1993. Available at http://www.math.uiuc.edu/Macaulay2/]) and explicit examples are enclosed. 相似文献
18.
Rick Miranda 《Advances in Mathematics》2005,198(2):439-447
We present a construction of the bielliptic surfaces as covers of certain rational elliptic surfaces. 相似文献
19.
Arthur Baragar 《Journal of Number Theory》2011,131(3):578-599
In this paper we show that, for a K3 surface within a certain class of surfaces and over a number field, the orbit of a point under the group of automorphisms is either finite or its exponent of growth is exactly the Hausdorff dimension of a fractal associated to the ample cone. In particular, the exponent depends on the geometry of the surface and not its arithmetic. For surfaces in this class, the exponent is 0.6527±0.0012. 相似文献
20.
《Mathematische Nachrichten》2017,290(14-15):2132-2153