共查询到20条相似文献,搜索用时 343 毫秒
1.
We introduce the notion of curve associated with a chain of blow-ups of a complex surface. On the basis of this notion, we classify elementary chains (of length up to seven) of blow-ups of the projective plane. We prove (under an additional condition) that the ramification curve of the inverse of a polynomial mapping cannot be isolated in 4 or 5 blow-ups. 相似文献
2.
Geometric and dynamic properties of embeddings of SL(2; ℤ) into the Cremona group are studied. Infinitely many nonconjugate
embeddings that preserve the type (i.e., that send elliptic, parabolic and hyperbolic elements onto elements of the same type)
are provided. The existence of infinitely many nonconjugate elliptic, parabolic and hyperbolic embeddings is also shown. In
particular, a group G of automorphisms of a smooth surface S obtained by blowing up 10 points of the complex projective plane is given. The group G is isomorphic to SL(2; ℤ), preserves an elliptic curve and all its elements of infinite order are hyperbolic. 相似文献
3.
Michael Lönne 《manuscripta mathematica》2000,103(4):455-464
The topological type of generalized Kummer surfaces is described in terms of sphere bundles over Riemann surfaces and the
complex projective plane. Explicit examples of sets of pairwise non-diffeomorphic K?hler surfaces of the same topological
type are given.
Received: 5 January 2000 相似文献
4.
平面上的射影变换,将二阶曲线变为另一二阶曲线,这个射影变换也可以称为这两个二阶曲线间的射影映射.若两个二阶曲线相切,则存在以切点为射影中心的两个二阶曲线间的射影映射;若两个二阶曲线相离,则存在以两个二阶曲线公切线交点为射影中心的射影映射;若两个二阶曲线相交,则存在以其中一交点为射影中心的两个二阶曲线间的射影映射. 相似文献
5.
Projective surfaces with bi-elliptic hyperplane sections 总被引:1,自引:0,他引:1
We study projective surfaces X which have a bi-elliptic curve (i.e. 2∶1 covering of an elliptic curve) among their hyperplane
sections . We give a complete characterization of those surfaces when their degree d is d≥17 (only conic bundles and scrolls
if d≥19, three possible exception otherwise) and when d≤8. A conjecture is given for the remaining cases. The main tool we
use is the study of the adjunction mapping on X. 相似文献
6.
7.
《Mathematische Nachrichten》2017,290(5-6):876-884
We prove that the locus of Hilbert schemes of n points on a projective K 3 surface is dense in the moduli space of irreducible holomorphic symplectic manifolds of that deformation type. The analogous result for generalized Kummer manifolds is proven as well. Along the way we prove an integral constraint on the monodromy group of generalized Kummer manifolds. 相似文献
8.
JongHae Keum 《Topology》2006,45(5):919-927
A fake projective plane is a compact complex surface (a compact complex manifold of dimension 2) with the same Betti numbers as the complex projective plane, but not isomorphic to the complex projective plane. As was shown by Mumford, there exists at least one such surface.In this paper we prove the existence of a fake projective plane which is birational to a cyclic cover of degree 7 of a Dolgachev surface. 相似文献
9.
Kapil Hari Paranjape 《Proceedings Mathematical Sciences》2002,112(3):383-391
A result of Belyi can be stated as follows. Every curve defined over a number field can be expressed as a cover of the projective
line with branch locus contained in a rigid divisor. We define the notion of geometrically rigid divisors in surfaces and
then show that every surface defined over a number field can be expressed as a cover of the projective plane with branch locus
contained in a geometrically rigid divisor in the plane. The main result is the characterization of arithmetically defined
divisors in the plane as geometrically rigid divisors in the plane. 相似文献
10.
We seek to characterize homology classes of Lagrangian projective spaces embedded in irreducible holomorphic‐symplectic manifolds, up to the action of the monodromy group. This paper addresses the case of manifolds deformation‐equivalent to the Hilbert scheme of length‐3 subschemes of a K3 surface. The class of the projective space in the cohomology ring has prescribed intersection properties, which translate into Diophantine equations. Possible homology classes correspond to integral points on an explicit elliptic curve; our proof entails showing that the only such point is two‐torsion. © 2011 Wiley Periodicals, Inc. 相似文献
11.
Yoshifumi Takeda Nara 《Mathematische Nachrichten》1994,167(1):313-329
Let X be a nonsingular relatively minimal projective surface over an algebraically closed field of characteristic p > 0. We call X a false hyperelliptic surface if X satisfies the following conditions: (1) c2(X) = 0, c1(X)2 = 0, dim Alb (X) = 1, and (2) All fibres of the Albanese mapping of X are rational curves with only one cusp of type xpv + yn = 0. In this article, we consider a false hyperelliptic surface whose Albanese mapping has a cross-section. We prove that every false hyperellyptic surface with section arises from an elliptic ruled surface and that every false hyperelliptic surface has an elliptic fibration with multiple fibre. Moreover, we construct an example of false hyperelliptic surface with section, whose elliptic fibration has a multiple fibre of supersingular elliptic curve of multiplicity pv (v > 1). 相似文献
12.
Tomokuni Takahashi 《Geometriae Dedicata》2011,154(1):183-206
We classify the certain type of relative quadric hypersurfaces of 3-dimensional projective space bundles over a projective
line or an elliptic curve whose fiber is the direct product of 2 projective lines. 相似文献
13.
Ronald D. Baker 《Journal of Combinatorial Theory, Series A》1978,25(2):193-195
An elliptic semiplane (symmetric group divisible design with λ1 = 1 and λ2 = 0) is constructed. This elliptic semiplane cannot be realized as a projective plane minus a Baer subset, and is the first elliptic semiplane constructed which has this property. 相似文献
14.
Augusto Nobile 《Geometriae Dedicata》2000,80(1-3):1-27
First, a modern presentation of the theory of the Halphen transform is given. This method associates to a plane projective curve C, once a general conic has been chosen, another birationally equivalent plane curve, whose singularities are simpler than those of C. Repeating, a curve is obtained whose only singularities are nodes. Next, it is studied how to apply this process to a family of plane curves. With this technique it is possible to transform a given family (with irreducible general member) into one where, generically, the curves are nodal. Finally, it is studied a similar process, called the Halphen–Picard transformation, for surfaces in three-space. By suitably reiterating this procedure, a surface can be transformed into a birationally equivalent one (in the same projective space), such that the sections with planes in a general pencil are, generically, nodal curves. 相似文献
15.
Tomokuni Takahashi 《Mathematische Nachrichten》2013,286(4):402-429
We classify the algebraic surfaces with Eisenbud‐Harris general fibration of genus 4 over a rational curve or an elliptic curve whose slope attains the lower bound. The classification of our surfaces is strongly related to the result of the classification for certain relative quadric hypersurfaces in 3‐dimensional projective space bundles over a rational curve and an elliptic curve. We further prove some results about the canonical maps, the quadric hulls of the canonical images and the deformation for these surfaces. 相似文献
16.
Daisuke Matsushita 《Mathematische Annalen》2001,321(4):755-773
We classify singular fibres over general points of the discriminant locus of projective Lagrangian fibrations over 4-dimensional
holomorphic symplectic manifolds. The singular fibre F is the following either one: F is isomorphic to the product of an elliptic curve and a Kodaira singular fibre up to finite unramified covering or F is a normal crossing variety consisting of several copies of a minimal elliptic ruled surface of which the dual graph is
Dynkin diagram of type or . Moreover, we show all types of the above singular fibres actually occur.
Received: 10 March 2000 / Revised version: 29 September 2000 / Published online: 24 September 2001 相似文献
17.
18.
We construct projective moduli spaces for torsion-free sheaves on noncommutative projective planes. These moduli spaces vary smoothly in the parameters describing the noncommutative plane and have good properties analogous to those of moduli spaces of sheaves over the usual (commutative) projective plane P2.The generic noncommutative plane corresponds to the Sklyanin algebra S=Skl(E,σ) constructed from an automorphism σ of infinite order on an elliptic curve E⊂P2. In this case, the fine moduli space of line bundles over S with first Chern class zero and Euler characteristic 1−n provides a symplectic variety that is a deformation of the Hilbert scheme of n points on P2?E. 相似文献
19.
Paola Parenti 《Geometriae Dedicata》2003,101(1):129-151
In 1974, Rokhlim introduced complex orientations for nonsingular real algebraic plane projective curves of type I. Here we give a definition of symmetric orientations and of "type" for T-curves which are PL-curves constructed using a combinatorial method called T-construction. An important aspect of T-construction is that, under particular conditions, the constructed T-curve has the isotopy type of a nonsingular real algebraic plane projective curve. T-construction is in fact a particular case of the method of construction of real algebraic projective varieties due to O. Ya. Viro. We prove that if an algebraic curve is associated to a T-curve by the Viro process, then the type of the T-curve coincides with the type of the algebraic curve and its symmetric orientations are complex orientations as defined by Rokhlin. The main result of this paper is the classification theorem for T-curves of type I. 相似文献
20.
Helmut Pottmann 《Monatshefte für Mathematik》1985,99(4):315-320
In accordance withH. R. Müller [3] we understand under a curve of constant slope in the elliptic 3-space an isogonal trajectory of the generators of an arbitrary Clifford cylinder. Using linegeometric methods in a special projective model, we study in particular those curves of constant slope, whose tangents form also a constant angle with a fixed plane. Thereby we meet with well-known classes of curves in the Euclidean space, such as spherical involutoids and tractrices of circles and loxodromes on a torus. 相似文献