共查询到20条相似文献,搜索用时 0 毫秒
1.
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
2.
In this paper, we investigate whether the 124 nonsingular toric Fano
4-folds admit totally nondegenerate embeddings from abelian surfaces or
not. In consequence, we determine the possibilities of these embeddings,
except for the remaining 18 nonsingular toric Fano 4-folds.
Received: 12 July 2002 相似文献
3.
Laura Costa 《manuscripta mathematica》1999,100(3):335-349
Let be a ruled Fano 3-fold. The goal of this paper is to compute the dimension, prove the irreducibility and smoothness and describe
the structure of the moduli space M
L
(2;c
1,c
2) of L-stable, rank 2 vector bundles E on X with certain Chern classes and for a suitable polarization L closely related to c
2. More precisely, we will cover the study of some moduli spaces M
L
(2;c
1,c
2) such that the generic point is given as a non-trivial extension of line bundles. This work nicely reflects the general philosophy that moduli spaces
inherits a lot of geometrical properties of the underlying variety.
Received: 16 February 1999 / Revised version: 2 July 1999 相似文献
4.
Andreas Leopold Knutsen 《manuscripta mathematica》2001,104(2):211-237
We give necessary and sufficient conditions for a big and nef line bundle L of any degree on a K3 surface or on an Enriques surface S to be k-very ample and k-spanned. Furthermore, we give necessary and sufficient conditions for a spanned and big line bundle on a K3 surface S to be birationally k-very ample and birationally k-spanned (our definition), and relate these concepts to the Clifford index and gonality of smooth curves in |L| and the existence of a particular type of rank 2 bundles on S. Received: 28 March 2000 / Revised version: 20 October 2000 相似文献
5.
We give a result that relates the diffeomorphism type of the link of a non-degenerate semi-quasi-homogeneous hypersurface simple K3 singularity with the singularities of the normal K 3 surface that appears as the exceptional divisor of the resolution of the singularity. As a result, we show that the links are diffeomorphic to the connected sum of copies of S2×S3. Moreover, we also show that the topological types of hypersurface simple K3 singularities defined by non-degenerate semi-quasi-homogeneous polynomials are all different. 相似文献
6.
We prove that for any of a wide class of elliptic surfaces X defined over a number field k, if there is an algebraic point on X that lies on only finitely many rational curves, then there is an algebraic point on X that lies on no rational curves. In particular, our theorem applies to a large class of elliptic K3 surfaces, which relates to a question posed by Bogomolov in 1981. 相似文献
7.
D.-Q. Zhang 《Journal of Pure and Applied Algebra》2006,207(1):119-138
In this note, we consider all possible extensions G of a non-trivial perfect group H acting faithfully on a K3 surface X. The pair (X,G) is proved to be uniquely determined by G if the transcendental value of G is maximum. In particular, we have , if H is the alternating group A5 and normal in G. 相似文献
8.
We show the nonvanishing of H
0(X,−K
X
) for any a Fano 3-fold X for which −K
X
is a multiple of another Weil divisor in Cl(X). The main case we study is Fano 3-folds with Fano index 2: that is, 3-folds X with rank Pic(X)=1, -factorial terminal singularities and −K
X
= 2A for an ample Weil divisor A. We give a first classification of all possible Hilbert series of such polarised varieties (X,A) and deduce both the nonvanishing of H
0(X,−K
X
) and the sharp bound (−K
X
)3≥ 8/165. We find the families that can be realised in codimension up to 4. 相似文献
9.
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 X → B 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
10.
11.
The aim of this work is to contribute to the classification of projective varieties according to their representation type, providing examples of n -dimensional varieties of wild representation type, for arbitrary n?2. More precisely, we prove that all Fano blow-ups of Pn at a finite number of points are of wild representation type exhibiting families of dimension of order r2 of simple (hence, indecomposable) ACM rank r vector bundles for any r?n. In the two dimensional case, the vector bundles that we construct are moreover Ulrich bundles and μ-stable with respect to certain ample divisor. 相似文献
12.
Daniel Allcock 《Mathematische Annalen》2000,317(3):483-488
13.
《Mathematische Nachrichten》2018,291(13):2084-2098
Consider an arbitrary automorphism of an Enriques surface with its lift to the covering K3 surface. We prove a bound of the order of the lift acting on the anti‐invariant cohomology sublattice of the Enriques involution. We use it to obtain some mod 2 constraint on the original automorphism. As an application, we give a necessary condition for Salem numbers to be dynamical degrees on Enriques surfaces and obtain a new lower bound on the minimal value. In the Appendix, we give a complete list of Salem numbers that potentially could be the minimal dynamical degree on Enriques surfaces and for which the existence of geometric automorphisms is unknown. 相似文献
14.
Paul Freitag 《Mathematische Annalen》1997,309(2):179-198
15.
Yoshiaki Fukuma 《Journal of Pure and Applied Algebra》2007,211(3):609-621
Let (X,L) be a polarized manifold of dimension n defined over the field of complex numbers. In this paper, we treat the case where n=3 and 4. First we study the case of n=3 and we give an explicit lower bound for h0(KX+L) if κ(X)≥0. Moreover, we show the following: if κ(KX+L)≥0, then h0(KX+L)>0 unless κ(X)=−∞ and h1(OX)=0. This gives us a partial answer of Effective Non-vanishing Conjecture for polarized 3-folds. Next for n=4 we investigate the dimension of H0(KX+mL) for m≥2. If n=4 and κ(X)≥0, then a lower bound for h0(KX+mL) is obtained. We also consider a conjecture of Beltrametti-Sommese for 4-folds and we can prove that this conjecture is true unless κ(X)=−∞ and h1(OX)=0. Furthermore we prove the following: if (X,L) is a polarized 4-fold with κ(X)≥0 and h1(OX)>0, then h0(KX+L)>0. 相似文献
16.
Marie José Bertin 《Journal of Number Theory》2008,128(11):2890-2913
17.
Yoshiaki Fukuma 《Journal of Pure and Applied Algebra》2011,215(2):168-184
Let X be a smooth complex projective variety of dimension 3 and let L be an ample line bundle on X. In this paper, we provide a lower bound for h0(m(KX+L)) under the assumption that κ(KX+L)≥0. In particular, we get the following: (1) if 0≤κ(KX+L)≤2, then h0(KX+L)>0 holds. (2) If κ(KX+L)=3, then h0(2(KX+L))≥3 holds. Moreover we get a classification of (X,L) with κ(KX+L)=3 and h0(2(KX+L))=3 or 4. 相似文献
18.
We study the geometry of the birational map between an intersection of a net of quadrics in
that contains a line and the double sextic branched along the discriminant of the net. We show that the branch locus of a
smooth double sextic S
6 is discriminant of a net of quadrics in
such that S
6 is isomorphic to the intersection of this net iff a certain configuration of rational curves on S6 is weakly even.
Received: 14 September 2005
Suported by the DFG Schwerpunktprogramm ‘Global methods in complex geometry’. The first named author is partially supported
by the KBN Grant No. 1 P03A 008 28. The second named author is partially supported by the KBN Grant No. 2 P03A 016 25. 相似文献
19.
Christophe Eyral 《Topology》2004,43(4):749-764
We express, under appropriate conditions, the fundamental group of a singular complex quasi-projective variety as a quotient of the fundamental group of a general hyperplane section, using a generic pencil. The subgroup by which the quotient is taken is described with the help of the monodromies around the exceptional hyperplanes of the pencil. This is a new generalization of the classical Zariski-van Kampen theorem on curves. 相似文献
20.
We show that for any metric space M satisfying certain natural conditions, there is a finitely generated group G, an ultrafilter ω, and an isometric embedding ι of M to the asymptotic cone Coneω(G) such that the induced homomorphism ι*:π1(M)→π1(Coneω(G)) is injective. In particular, we prove that any countable group can be embedded into a fundamental group of an asymptotic cone of a finitely generated group. 相似文献