共查询到20条相似文献,搜索用时 15 毫秒
1.
We discuss a notion of large complex structure for elliptic K3 surfaces with section inspired by the eight-dimensional F-theory/heterotic duality in string theory. This concept is naturally associated with the Type II Mumford partial compactification of the moduli space of periods for these structures. The paper provides an explicit Hodge-theoretic condition for the complex structure of an elliptic K3 surface with section to be large. We also establish certain geometric consequences of this large complex structure condition in terms of the Kodaira types of the singular fibers of the elliptic fibration. 相似文献
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Let be a surface in given by the intersection of a (1,1)-form and a (2,2)-form. Then is a K3 surface with two noncommuting involutions and . In 1991 the second author constructed two height functions and which behave canonically with respect to and , and in 1993 together with the first author showed in general how to decompose such canonical heights into a sum of local heights . We discuss how the geometry of the surface is related to formulas for the local heights, and we give practical algorithms for computing the involutions , , the local heights , , and the canonical heights , .
5.
Naoki Murabayashi 《Journal of Number Theory》2004,108(2):268-286
The purpose of this paper is to decide the conditions under which a CM elliptic curve is modular over its field of definition. 相似文献
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AbstractIn this paper, we provide a complete classification of non-symplectic automorphisms of order 9 of complex K3 surfaces. 相似文献
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Jonas Baltes 《Mathematische Nachrichten》2023,296(7):2701-2714
We show that on every elliptic K3 surface there are rational curves such that , that is, of unbounded arithmetic genus. Moreover, we show that the union of the lifts of these curves to is dense in the Zariski topology. As an application, we give a simple proof of a theorem of Kobayashi in the elliptic case, that is, there are no globally defined symmetric differential forms. 相似文献
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Yukinobu Toda 《Advances in Mathematics》2008,217(6):2736-2781
For a K3 surface X and its bounded derived category of coherent sheaves D(X), we have the notion of stability conditions on D(X) in the sense of T. Bridgeland. In this paper, we show that the moduli stack of semistable objects in D(X) with a fixed numerical class and a phase is represented by an Artin stack of finite type over C. Then following D. Joyce's work, we introduce the invariants counting semistable objects in D(X), and show that the invariants are independent of a choice of a stability condition. 相似文献
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No Abstract. .
Received: October 2004 Revision: May 2005 Accepted: July 2005
The second author was partially supported by NSF grant DMS-0304587. 相似文献
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Christophe Breuil Brian Conrad Fred Diamond Richard Taylor 《Journal of the American Mathematical Society》2001,14(4):843-939
We complete the proof that every elliptic curve over the rational numbers is modular.
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Nikulin has classified all finite abelian groups acting symplectically on a K3 surface and he has shown that the induced action on the K3 lattice U 3 ⊕ E 8(?1)2 depends only on the group but not on the K3 surface. For all the groups in the list of Nikulin we compute the invariant sublattice and its orthogonal complement by using some special elliptic K3 surfaces. 相似文献
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Paolo Stellari 《Transactions of the American Mathematical Society》2008,360(12):6631-6642
We consider the natural action of a finite group on the moduli space of polarized K3 surfaces which induces a duality defined by Mukai for surfaces of this type. We show that the group permutes polarized Fourier-Mukai partners of polarized K3 surfaces and we study the divisors in the fixed loci of the elements of this finite group.
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《Journal of Pure and Applied Algebra》2023,227(3):107215
If a K3 surface admits an automorphism with a Siegel disk, then its Picard number is an even integer between 0 and 18. Conversely, using the method of hypergeometric groups, we are able to construct K3 surface automorphisms with Siegel disks that realize all possible Picard numbers. The constructions involve extensive computer searches for appropriate Salem numbers and computations of algebraic numbers arising from holomorphic Lefschetz-type fixed point formulas and related Grothendieck residues. 相似文献
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Alessandra Sarti 《Mathematische Nachrichten》2008,281(7):1031-1046
In a previous paper, [12], we described six families of K 3‐surfaces (over ?) with Picard‐number 19, and we identified surfaces with Picard‐number 20. In these notes we classify some of the surfaces by computing their transcendental lattices. Moreover, we show that the surfaces with Picard‐number 19 are birational to a Kummer surface which is the quotient of a non‐product type abelian surface by an involution. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
15.
Alice Garbagnati 《代数通讯》2013,41(2):583-616
We analyze K3 surfaces admitting an elliptic fibration ? and a finite group G of symplectic automorphisms preserving this elliptic fibration. We construct the quotient elliptic fibration ?/G comparing its properties to the ones of ?. We show that if ? admits an n-torsion section, its quotient by the group of automorphisms induced by this section admits again an n-torsion section, and we describe the coarse moduli space of K3 surfaces with a given finite group contained in the Mordell–Weil group. Considering automorphisms coming from the base of the fibration, we find the Mordell–Weil lattice of a fibration described by Kloosterman, and we find K3 surfaces with dihedral groups as group of symplectic automorphisms. We prove the isometries between lattices described by the author and Sarti and lattices described by Shioda and by Greiss and Lam. 相似文献
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Let X be a K3 surface over a number field K. We prove that there exists a finite algebraic field extension E/K such that X has ordinary reduction at every non-archimedean place of E outside a density zero set of places.
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We determine the necessary and sufficient conditions on the entries of the intersection matrix of the transcendental lattice of a singular K3 surface for the surface to doubly cover an Enriques surface.
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Shingo Taki 《Mathematische Nachrichten》2011,284(1):124-135
In this paper, we study non‐symplectic automorphisms of order 3 on algebraic K3 surfaces over ${\bb C}$ which act trivially on the Néron‐Severi lattice. In particular we shall characterize their fixed loci in terms of the invariants of 3‐elementary lattices. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim 相似文献
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Using the Dieudonné theory we will study a reduction of an abelian variety with complex multiplication at a prime. Our results may be regarded as generalization of the classical theorem due to Deuring for CM-elliptic curves. We will also discuss a sufficient condition for a prime at which the reduction of a CM-curve is maximal. 相似文献
20.
Arthur Baragar 《Compositio Mathematica》2003,137(2):115-134
In this paper, we study the family of algebraic K3 surfaces generated by the smooth intersection of a (1, 1) form and a (2, 2) form in
defined over
and with Picard number 3. We describe the group of automorphisms
on V. For an ample divisor D and an arbitrary curve C
0 on V, we investigate the asymptotic behavior of the quantity
. We show that the limit
exists, does not depend on the choice of curve C or ample divisor D, and that .6515<<.6538. 相似文献