共查询到20条相似文献,搜索用时 15 毫秒
1.
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
2.
Celalettin Kaya 《代数通讯》2013,41(3):1173-1178
We investigate the problem of lifting fibrations of genus one on algebraic surfaces of Kodaira dimension zero. We prove that fibrations on the following surfaces lift: Enriques surfaces, K3 surfaces covering Enriques surfaces, certain hyperelliptic, and quasi-hyperelliptic surfaces. 相似文献
3.
Sultan Erdoğan Demir 《Topology and its Applications》2012,159(10-11):2580-2591
We compute the monodromy groups of real Enriques surfaces of hyperbolic type. The principal tools are the deformation classification of such surfaces and a modified version of Donaldson?s trick, relating real Enriques surfaces and real rational surfaces. 相似文献
4.
Taro HAYASHI 《数学年刊B辑(英文版)》2023,44(1):99-162
The quotient space of a K3 surface by a finite group is an Enriques surface or a rational surface if it is smooth. Finite groups where the quotient space are Enriques surfaces are known. In this paper, by analyzing effective divisors on smooth rational surfaces, the author will study finite groups which act faithfully on K3 surfaces such that the quotient space are smooth. In particular, he will completely determine effective divisors on Hirzebruch surfaces such that there is a finite Abelian co... 相似文献
5.
《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
6.
In this paper, we prove the existence of an Enriques surface with a polarization of degree four with an Ulrich bundle of rank one. As a consequence, we prove that general polarized Enriques surfaces of degree four, with the same numerical polarization class, carry Ulrich line bundles. 相似文献
7.
Samuel Boissière Marc Nieper-Wißkirchen Alessandra Sarti 《Journal de Mathématiques Pures et Appliquées》2011,95(5):553-563
We define Enriques varieties as a higher dimensional generalization of Enriques surfaces and construct examples by using fixed point free automorphisms on generalized Kummer varieties. We also classify all automorphisms of generalized Kummer varieties that come from an automorphism of the underlying abelian surface. 相似文献
8.
For a real Enriques surface Y we prove that every homology class in H1(Y (R), Z/2) can be represented by a real algebraic curve if and only if all connected components of Y(R) are orientable. Furthermore, we give a characterization of real Enriques surfaces which are Galois-Maximal and/or Z-Galois-Maximal and we determine the Brauer group of any real Enriques surface Y. 相似文献
9.
The Enriques log surfaces with δ= 1 are classified. 相似文献
10.
We consider the class of singular double coverings \(X \rightarrow {\mathbb {P}}^3\) ramified in the degeneration locus \(D\) of a family of 2-dimensional quadrics. These are precisely the quartic double solids constructed by Artin and Mumford as examples of unirational but nonrational conic bundles. With such a quartic surface \(D,\) one can associate an Enriques surface \(S\) which is the factor of the blowup of \(D\) by a natural involution acting without fixed points (such Enriques surfaces are known as nodal Enriques surfaces or Reye congruences). We show that the nontrivial part of the derived category of coherent sheaves on this Enriques surface \(S\) is equivalent to the nontrivial part of the derived category of a minimal resolution of singularities of \(X\). 相似文献
11.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1997,324(3):317-322
We introduce a new invariant, Pontryagin-Viro form, of real algebraic surfaces. We evaluate it for real Enriques surfaces with non-negative minimal Euler characteristic of the components of the real part and prove that, when combined with the known topological invariants, it distinguishes the deformation types of such surfaces. 相似文献
12.
Kōta Yoshioka 《Compositio Mathematica》2003,138(3):261-288
In this paper, we consider the preservation of stability by using the notion of twisted stability. As applications, (1) we show that moduli spaces of stable sheaves on K3 and abelian surfaces are irreducible and (2) we compute Hodge polynomials of some moduli spaces of stable sheaves on Enriques surfaces. 相似文献
13.
We shall give a proof for Vorontsov's Theorem and apply this to classify log Enriques surfaces with large prime canonical index.
14.
Tomasz Szemberg 《Transactions of the American Mathematical Society》2001,353(12):4963-4972
We study linear systems on Enriques surfaces. We prove rationality of Seshadri constants of ample line bundles on Enriques surfaces and provide lower bounds on these numbers. We show the nonexistence of -very ample line bundles on Enriques surfaces of degree for , thus answering an old question of Ballico and Sommese.
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16.
Gert Monstad Hana 《Mathematische Nachrichten》2006,279(3):242-254
We study Cossec's ? ‐function, which is defined for divisors with positive self‐intersection on an Enriques surface. In this paper we study the existence of pairs (C 2, ? (C )) with C an irreducible curve. The ? ‐function gives in a natural way scrolls containing Enriques surfaces. We compute scroll types to some of these scrolls. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
17.
We classify logarithmic Enriques surfaces with = 2 相似文献
18.
Archiv der Mathematik - In this short note, I point out that results of Ballico and Kool–Shende–Thomas together imply that on K3, Enriques, and Abelian surfaces, if L is a very ample... 相似文献
19.
S. Zube 《Mathematical Notes》1997,61(6):693-699
The main purpose of this paper is to study exceptional vector bundles on Enriques surfaces.
Translated fromMatematicheskie Zametki, Vol. 61, No. 6, pp. 825–834, June, 1997. 相似文献
20.
Ciro Ciliberto Thomas Dedieu Concettina Galati Andreas Leopold Knutsen 《Mathematische Nachrichten》2023,296(2):574-587
We prove that certain Severi varieties of nodal curves of positive genus on general blow-ups of the twofold symmetric product of a general elliptic curve are nonempty and smooth of the expected dimension. This result, besides its intrinsic value, is an important preliminary step for the proof of nonemptiness of Severi varieties on general Enriques surfaces. 相似文献