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1.
We show that if a smooth projective 4-fold M contains an ample divisor A which is P 1-bundle π :AS over a smooth projective surface S, π is extended to a P 2-bundle π :SS, unless $A$ is isomorphic to P 2×P 1. Received: 28 September 1998 / Revised version: 16 August 1999  相似文献   

2.
Let X be a smooth projective curve defined over an algebraically closed field of positive characteristic. We give a necessary and sufficient condition for a vector bundle over X to be ample. This generalizes a criterion given by Lange in [Math. Ann. 238 (1978) 193-202] for a rank two vector bundle over X to be ample.  相似文献   

3.
关于Extremal Ray的除子型收缩   总被引:2,自引:0,他引:2  
赵逸才 《数学进展》2001,30(6):557-566
设X是定义在复数域上的n维光滑射影簇且它的典范除子Kx不是数字有效的,A是X上的一个ample除子。本文详细研究了由Kx (n-k)A确定的关于X的除子型收缩映射(1≤k≤n-1),对其例外休的结构作了比较完整的分类,特别地,当1≤k≤3时,即得到Fujita,Sommese等人的相关结果。  相似文献   

4.
Let be a smooth complex projective hypersurface. In this paper we show that, if the degree of X is large enough, then there exist global sections of the bundle of invariant jet differentials of order n on X, vanishing on an ample divisor. We also prove a logarithmic version, effective in low dimension, for the log-pair , where D is a smooth irreducible divisor of high degree. Moreover, these result are sharp, i.e. one cannot have such jet differentials of order less than n.  相似文献   

5.
Let X be a smooth n-dimensional projective variety defined over and let L be a line bundle on X. In this paper we shall construct a moduli space parametrizing -cohomology L-twisted Higgs pairs, i.e., pairs where E is a vector bundle on X and . If we take , the canonical line bundle on X, the variety is canonically identified with the cotangent bundle of the smooth locus of the moduli space of stable vector bundles on X and, as such, it has a canonical symplectic structure. We prove that, in the general case, in correspondence to the choice of a non-zero section , one can define, in a natural way, a Poisson structure on . We also analyze the relations between this Poisson structure on and the canonical symplectic structure of the cotangent bundle to the smooth locus of the moduli space of parabolic bundles over X, with parabolic structure over the divisor D defined by the section s. These results generalize to the higher dimensional case similar results proved in [Bo1] in the case of curves. Received November 4, 1997; in final form May 28, 1998  相似文献   

6.
Let π : XY be the blow-up of a four-dimensional complex manifold Y along a smooth curve C. Assume that X is a Fano manifold and has another (3,1)-type extremal contraction ${\varphi : X \to Z}$ whose exceptional divisor meet that of the blow-up π : XY. We show that if the exceptional divisor of ${\varphi}$ is smooth, then Y is isomorphic to four-dimensional projective space and C is an elliptic curve of degree 4.  相似文献   

7.
We construct natural maps (the Klein and Wirtinger maps) from moduli spaces of semistable vector bundles over an algebraic curve X to affine spaces, as quotients of the nonabelian theta linear series. We prove a finiteness result for these maps over generalized Kummer varieties (moduli space of torus bundles), leading us to conjecture that the maps are finite in general. The conjecture provides canonical explicit coordinates on the moduli space. The finiteness results give low-dimensional parametrizations of Jacobians (in for generic curves), described by 2Θ functions or second logarithmic derivatives of theta.We interpret the Klein and Wirtinger maps in terms of opers on X. Opers are generalizations of projective structures, and can be considered as differential operators, kernel functions or special bundles with connection. The matrix opers (analogues of opers for matrix differential operators) combine the structures of flat vector bundle and projective connection, and map to opers via generalized Hitchin maps. For vector bundles off the theta divisor, the Szegö kernel gives a natural construction of matrix oper. The Wirtinger map from bundles off the theta divisor to the affine space of opers is then defined as the determinant of the Szegö kernel. This generalizes the Wirtinger projective connections associated to theta characteristics, and the associated Klein bidifferentials.  相似文献   

8.
LetX be a complex projective variety with log terminal singularities admitting an extremal contraction in terms of Minimal Model Theory, i.e. a projective morphism φ:XZ onto a normal varietyZ with connected fibers which is given by a (high multiple of a) divisor of the typeK x+rL, wherer is a positive rational number andL is an ample Cartier divisor. We first prove that the dimension of anu fiberF of φ is bigger or equal to (r-1) and, if φ is birational, thatdimF≥r, with the equalities if and only ifF is the projective space andL the hyperplane bundle (this is a sort of “relative” version of a theorem of Kobayashi-Ochiai). Then we describe the structure of the morphism φ itself in the case in which all fibers have minimal dimension with the respect tor. If φ is a birational divisorial contraction andX has terminal singularities we prove that φ is actually a “blow-up”.  相似文献   

9.
Over a smooth complex projective curve of genus ≥3, we study 1-cycles on the moduli space of rank-2 stable vector bundles with fixed determinant of degree 1. We show the first Chow group of the moduli space is isomorphic to the zeroth Chow group of the curve.  相似文献   

10.
Let X be a smooth complex projective variety with Neron–Severi group isomorphic to ℤ, and D an irreducible divisor with normal crossing singularities. Assume 1<r≤ 3. We prove that if π1(X) doesn't have irreducible PU(r) representations, then π1(X- D) doesn't have irreducible U(r) representations. The proof uses the non-existence of certain stable parabolic bundles. We also obtain a similar result for GL(2) when D is smooth. Received: 20 December 1999 / Revised version: 7 May 2000  相似文献   

11.
A determination of the fixed components, base points and irregularity is made for arbitrary numerically effective divisors on any smooth projective rational surface having an effective anticanonical divisor. All of the results are proven over an algebraically closed field of arbitrary characteristic. Applications, to be treated in separate papers, include questions involving: points in good position, birational models of rational surfaces in projective space, and resolutions for 0-dimensional subschemes of defined by complete ideals.

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12.
We consider the surface obtained from the projective plane by blowing up the points of intersection of two plane curves of same degree meeting transversely. We find minimal free resolutions of the defining ideals of these surfaces embedded in projective space by the sections of a very ample divisor class. All of the results are proven over an algebraically closed field of arbitrary characteristic.  相似文献   

13.
Let X be an algebraic submanifold of the complex projective space $\mathbb{P}^N$ of dimension $n \geq 5$. We describe those $X \subset \mathbb{P}^N$ whose intersection with some hyperplane is a smooth simply normal crossing divisor $A_{1} + \cdots + A_{r}$ with $r \geq 2$ such that $g(A_{k}, L_{A_k}) \leq 1$ for $k=1,\ldots, r$.Received: 14 December 2001  相似文献   

14.
Let be a very ample vector bundle of rank two on a smooth complex projective threefold X. An inequality about the third Segre class of is provided when is nef but not big, and when a suitable positive multiple of defines a morphism XB with connected fibers onto a smooth projective curve B, where KX is the canonical bundle of X. As an application, the case where the genus of B is positive and has a global section whose zero locus is a smooth hyperelliptic curve of genus ≧ 2 is investigated, and our previous result is improved for threefolds. Received: 27 January 2005; revised: 26 March 2005  相似文献   

15.
The purpose of this paper is to classify ample and spanned vector bundles of top Chern number two on smooth projective varieties of arbitrary dimension defined over an algebraically closed field of characteristic zero.

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16.
In this paper we study defining equations and syzygies among them of projective bundles. We prove that for a given p≥0, if a vector bundle on a smooth complex projective variety is sufficiently ample, then the embedding given by the tautological line bundle satisfies property Np.  相似文献   

17.
Taro Hayashi 《代数通讯》2019,47(1):230-235
We consider the quotient space of an abelian surface by a finite subgroup of the automorphism group. We classify the analytic representation of the group and the branch divisor of the natural projection to the quotient space, where the quotient space is isomorphic to the product of the projective lines.  相似文献   

18.
By a recent result of Viehweg, projective manifolds with ample canonical class have a coarse moduli space, which is a union of quasiprojective varieties.In this paper, we prove that there are manifolds with ample canonical class that lie on arbitrarily many irreducible components of the moduli; moreover, for any finite abelian group G there exist infinitely many components M of the moduli of varieties with ample canonical class such that the generic automorphism group GMis equal to G. In order to construct the examples, we use abelian covers. Let Y be a smooth complex projective variety of dimension ? 2. A Galois cover f :X ? Y whose Galois group is finite and abelian is called an abelian cover of Y; by [Pal], it is determined by its building data, i.e. by the branch divisors and by some line bundles on Y, satisfying appropriate compatibility conditions. Natural deformations of an abelian cover are also introduced in [Pal]. In this paper we prove two results about abelian covers:first, that if the building data are sufficiently ample, then the natural deformations surject on the Kuranishi family of X; second, that if the building data are sufficiently ample and generic, then Aut(X)= G.  相似文献   

19.
In this paper a numerical criterion for divisors on a smooth projective surface to be very ample is given. The idea is to restrict a given divisor to a sufficient number of (not necessarily, irreducible nor reduced) curfes on the surface and prove the very ampleness of the restriction. At the end we given an application to Bordiga surfaces.  相似文献   

20.
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