共查询到20条相似文献,搜索用时 15 毫秒
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A map is constructed from the moduli of hyper-Kähler tori to hyper-Kähler K3 surfaces which does not coincide with the Kummer map. The map takes a torus to the moduli space of SO(3) connections on a bundle with nontrivial first Stiefel-Whitney class and first Pontrjagin class equal to –4. This map is shown to intersect the Kummer moduli and also certain subvarieties of singular K3 surfaces. Our map is shown to satisfy the local Torelli theorem, and the K3-surfaces in its image are shown to carry a natural metric which is Calabi-Yau. 相似文献
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Kristina Frantzen 《Mathematische Annalen》2011,350(4):757-791
K3-surfaces with antisymplectic involution and compatible symplectic actions of finite groups are considered. In this situation
actions of large finite groups of symplectic transformations are shown to arise via double covers of Del Pezzo surfaces, and
a complete classification of K3-surfaces with maximal symplectic symmetry is obtained. 相似文献
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Siman Wong 《manuscripta mathematica》2000,102(1):129-137
Given a prime l and an elliptic curve E defined over a number field k, we show that a non-zero point P] E(k) lies in lE(k) if and only if P lies in lE(k)(mod ) for almost all finite primes of k. We give conditions on l under which analogous results hold for Abelian varieties and with one point replaced by a finite number of points. We also construct examples to show that these conditions are essential. 相似文献
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Yu. G. Zarkhin 《Mathematical Notes》1976,19(3):240-244
In this paper Tate's finiteness conjecture for isogenies of polarized Abelian varieties in characteristic p>2 is proved. From this conjecture it is deduced that Tate modules are semisimple and that Tate's conjecture on the homomorphisms of Abelian varieties is valid.Translated from Matematicheskie Zametki, Vol. 19, No. 3, pp. 393–400, March, 1976. 相似文献
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Gian Pietro Pirola 《Mathematische Annalen》1988,282(3):361-368
This work was done while the author was visiting the Brown University Providence, R.I., USA. 相似文献
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We study certain groupoids generating Abelian, strongly Abelian, and Hamiltonian varieties. An algebra is Abelian if t( a,[`(c)] ) = t( a,[`(d)] ) ? t( b,[`(c)] ) = t( b,[`(d)] ) t\left( {a,\bar{c}} \right) = t\left( {a,\bar{d}} \right) \to t\left( {b,\bar{c}} \right) = t\left( {b,\bar{d}} \right) for any polynomial operation on the algebra and for all elements a, b, [`(c)] \bar{c} , [`(d)] \bar{d} . An algebra is strongly Abelian if t( a,[`(c)] ) = t( b,[`(d)] ) ? t( e,[`(c)] ) = t( e,[`(d)] ) t\left( {a,\bar{c}} \right) = t\left( {b,\bar{d}} \right) \to t\left( {e,\bar{c}} \right) = t\left( {e,\bar{d}} \right) for any polynomial operation on the algebra and for arbitrary elements a, b, e, [`(c)] \bar{c} , [`(d)] \bar{d} . An algebra is Hamiltonian if any subalgebra of the algebra is a congruence class. A variety is Abelian (strongly Abelian,
Hamiltonian) if all algebras in a respective class are Abelian (strongly Abelian, Hamiltonian). We describe semigroups, groupoids
with unity, and quasigroups generating Abelian, strongly Abelian, and Hamiltonian varieties. 相似文献
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M. Somekawa 《K-Theory》1990,4(2):105-119
In this paper we define and study a Milnor K-group attached to a finite family of semi-Abelian varieties over a field, which is a generalization of the usual Milnor K-group. Using this group, we generalize the work of Bloch. 相似文献
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Salman Abdulali 《Compositio Mathematica》1997,109(3):341-355
We investigate the relationship between the usual and general Hodgeconjectures for abelian varieties. For certain abelian varieties A, weshow that the usual Hodge conjecture for all powers of A implies thegeneral Hodge conjecture for A. 相似文献
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Efficient pairing computation on supersingular Abelian varieties 总被引:2,自引:0,他引:2
Paulo S. L. M. Barreto Steven D. Galbraith Colm Ó’ hÉigeartaigh Michael Scott 《Designs, Codes and Cryptography》2007,42(3):239-271
We present a general technique for the efficient computation of pairings on Jacobians of supersingular curves. This formulation,
which we call the eta pairing, generalizes results of Duursma and Lee for computing the Tate pairing on supersingular elliptic
curves in characteristic 3. We then show how our general technique leads to a new algorithm which is about twice as fast as
the Duursma–Lee method. These ideas are applied to elliptic and hyperelliptic curves in characteristic 2 with very efficient
results. In particular, the hyperelliptic case is faster than all previously known pairing algorithms.
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