共查询到20条相似文献,搜索用时 312 毫秒
1.
Hiroyuki Ito 《Mathematische Nachrichten》2010,283(7):1037-1053
In this paper, we study the Mordell‐Weil lattices of the family of elliptic surfaces which is arising from the E84 singularity, one of the ADE singularities in characteristic 2. And we construct a subfamily of the universal family of supersingular K 3 surfaces in characteristic 2 as an application (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
2.
Ursula Whitcher 《代数通讯》2013,41(4):1427-1440
We consider the symplectic action of a finite group G on a K3 surface X. The Picard group of X has a primitive sublattice determined by G. We show how to compute the rank and discriminant of this sublattice. We then investigate the classification of symplectic actions by a fixed finite group, using moduli spaces of K3 surfaces with symplectic G-action. 相似文献
3.
Let G be a connected reductive linear algebraic group over , and X a compact connected Riemann surface. Let be a Levi factor of some parabolic subgroup of G, with its maximal abelian quotient. We prove that a holomorphic G-bundle over X admits a flat connection if and only if for every such L and every reduction of the structure group of to L, the -bundle obtained by extending the structure group of is topologically trivial. For , this is a well-known result of A. Weil.
Received: 1 December 2000 / Revised version: 2 April 2001 / Published online: 24 September 2001 相似文献
4.
In this article we construct an infinite family of simply connected minimal symplectic 4-manifolds, each of which admits at
least two nonisomorphic Lefschetz fibration structures with the same generic fiber. We obtain such examples by performing
knot surgery on an elliptic surface E(n) using a special type of 2-bridge knots.
This work was supported by grant No. R01-2005-000-10625-0 from the KOSEF and by the Korea Research Foundation Grant funded
by the Korean Government (KRF-2007-314-C00024). 相似文献
5.
Let G be a finitely presentable group. We provide an infinite family of homeomorphic but pairwise non-diffeomorphic, symplectic but non-complex closed 4-manifolds with fundamental group G such that each member of the family admits a Lefschetz fibration of the same genus over the two-sphere. As a corollary, we also show the existence of a contact 3-manifold which admits infinitely many homeomorphic but pairwise non-diffeomorphic Stein fillings such that the fundamental group of each filling is isomorphic to G. Moreover, we observe that the contact 3-manifold above is contactomorphic to the link of some isolated complex surface singularity equipped with its canonical contact structure. 相似文献
6.
Pham Huu Tiep 《Mathematische Nachrichten》1997,184(1):313-327
The notion of globally irreducible representations of finite groups was introduced by B.H. Gross, in order to explain new series of Euclidean lattices discovered recently by N. Elkies and T. Shioda using Mordell–Weil lattices of elliptic curves. It has been observed by R. Gow and Gross that irreducible Weil representations of certain finite classical groups lead to globally irreducible representations. In this paper we classify all globally irreducible representations coming from Weil representations of finite classical groups. 相似文献
7.
Cheng Gong 《代数通讯》2020,48(2):724-732
AbstractIn this article, we give a new upper bound for the Mordell–Weil rank of a surface fibration and we prove an analog result in positive characteristic. 相似文献
8.
Alice Garbagnati 《Geometriae Dedicata》2010,145(1):219-232
Nikulin proved that the isometries induced on the second cohomology group of a K3 surface X by a finite abelian group G of symplectic automorphisms are essentially unique. Moreover he computed the discriminant of the sublattice of
H2(X,\mathbbZ){H^2(X,\mathbb{Z})} which is fixed by the isometries induced by G. However for certain groups these discriminants are not the same as those found for explicit examples. Here we describe Kummer
surfaces for which this phenomena happens and we explain the difference. 相似文献
9.
Sara Arias‐de‐Reyna Wojciech Gajda Sebastian Petersen 《Mathematische Nachrichten》2013,286(13):1269-1286
In this paper we prove the Geyer‐Jarden conjecture on the torsion part of the Mordell‐Weil group for a large class of abelian varieties defined over finitely generated fields of arbitrary characteristic. The class consists of all abelian varieties with big monodromy, i.e., such that the image of Galois representation on ?‐torsion points, for almost all primes ?, contains the full symplectic group. 相似文献
10.
Fabienne Chouraqui 《代数通讯》2018,46(11):4710-4723
The structure group G of a non-degenerate symmetric set (X,S) is a Bieberbach and a Garside group. We describe a combinatorial method to compute explicitly a group of automorphisms of G and show this group admits a subgroup that preserves the Garside structure. In some special cases, we could also prove the group of automorphisms found is an outer automorphism group. 相似文献
11.
S. Cantat 《Transformation Groups》2001,6(3):201-214
We study the dynamics of the automorphisms group of K3 surfaces. Assuming that the surface contains two elliptic fibrations that are invariant by non-periodic automorphisms, we give the classification of invariant probability measures. We also describe the closure of orbits and then give applications to the repartition of rational points on K3 surfaces. 相似文献
12.
A. Wootton 《Israel Journal of Mathematics》2007,157(1):103-122
We determine a method to find explicit defining equations for each compact Riemann surface which admits a cyclic group of
automorphisms C
p
of prime order p such that the quotient space has genus 0. 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.
We establish new upper bounds for the height of the S-integral points of an elliptic curve. This bound is explicitly given in terms of the set S of places of the number field K involved, but also in terms of the degree of K, as well as the rank, the regulator and the height of a basis of the Mordell–Weil group of the curve. The proof uses the elliptic analogue of Baker’s method, based on lower bounds for linear forms in elliptic logarithms. 相似文献
15.
The quotient ℝ/G of the additive group of the reals modulo a countable subgroup G does not admit nontrivial Baire measurable automorphisms. 相似文献
16.
Martin R. Pettet 《Archiv der Mathematik》2006,86(1):26-30
If an infinite group G admits a free action by a group of automorphisms A which is virtually an FC-group and which has only finitely many orbits,
then G is isomorphic to the additive group of a field and the action is that of a group of semilinear transformations.
Received: 21 February 2005 相似文献
17.
18.
Pham Huu Tiep 《Geometriae Dedicata》1997,64(1):85-123
The notion of globally irreducible representations of finite groups has been introduced by B. H. Gross, in order to explain new series of Euclidean lattices discovered recently by N. Elkies and T. Shioda using Mordell--Weil lattices of elliptic curves. In this paper we first give a necessary condition for global irreducibility. Then we classify all globally irreducible representations of L
2(q) and 2B2(q), and of the majority of the 26 sporadic finite simple groups. We also exhibit one more globally irreducible representation, which is related to the Weil representation of degree (pn-1)/2 of the symplectic group Sp2n(p) (p 1 (mod 4) is a prime). As a consequence, we get a new series of even unimodular lattices of rank 2(pn–1). A summary of currently known globally irreducible representations is given. 相似文献
19.
20.
We consider K3 surfaces which are double covers of rational elliptic surfaces. The former are endowed with a natural elliptic fibration, which is induced by the latter. There are also other elliptic fibrations on such K3 surfaces, which are necessarily induced by special linear systems on the rational elliptic surfaces. We describe these linear systems. In particular, we observe that every conic bundle on the rational surface induces a genus 1 fibration on the K3 surface and we classify the singular fibers of the genus 1 fibration on the K3 surface it terms of singular fibers and special curves on the conic bundle on the rational surface. 相似文献