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1.
The aim of this paper is to construct non-trivial cycles in the first higher Chow group of the Jacobian of a curve having special torsion points. The basic tool is to compute the analogue of the Griffiths infinitesimal invariant of the natural normal function defined by the cycle as the curve moves in the corresponding moduli space. We prove also a Torelli-like theorem. The case of genus 2 is considered in the last section. To the memory of Fabio BardelliMathematics Subject Classification (2000) 14C25, 14C34 相似文献
2.
Pavlos Tzermias 《Proceedings of the American Mathematical Society》1997,125(3):663-668
Let denote the Jacobian of the Fermat curve of exponent 5 and let . We compute the groups , , , where is the unique quadratic subfield of . As an application, we present a new proof that there are no -rational points on the 5-th Fermat curve, except the so called ``points at infinity".
3.
4.
Hizuru Yamagishi 《Journal of Number Theory》2003,100(2):295-306
In this paper, we show that a special case of Lang's conjecture on rational points on surfaces of general type implies that there exist only finitely many elliptic curves, when the x-coordinates of n rational points are specified with n?8. 相似文献
5.
Pol Vanhaecke 《Acta Appl Math》1995,40(2):143-172
In this paper, a one-dimensional family of stratifications on a hyperelliptic Jacobian is introduced. It generalizes a well-known
stratification, considered in algebraic geometry, in the context of special divisors. The stratification is shown to be related
to a natural stratification on the Sato Grassmannian, via an extension of Krichever's map. It is also related to the stratification
associated to the Laurent solutions of certain vector fields which can both be seen as living on the Grassmannian or on the
Jacobian. 相似文献
6.
Jiangwei Xue 《Journal of Number Theory》2011,131(2):332-342
Text
Let p be a prime, and q a power of p. Using Galois theory, we show that over a field K of characteristic zero, the endomorphism algebras of the Jacobians of certain superelliptic curves yq=f(x) are products of cyclotomic fields.Video
For a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=z5ZzOy1K_Ec. 相似文献7.
A search for prime factors of the generalized Fermat numbers has been carried out for all pairs with and GCD. The search limit on the factors, which all have the form , was for and for . Many larger primes of this form have also been tried as factors of . Several thousand new factors were found, which are given in our tables.-For the smaller of the numbers, i.e. for , or, if , for , the cofactors, after removal of the factors found, were subjected to primality tests, and if composite with , searched for larger factors by using the ECM, and in some cases the MPQS, PPMPQS, or SNFS. As a result all numbers with are now completely factored.
8.
Eduardo Esteves 《Geometriae Dedicata》2009,139(1):167-181
A curve, that is, a connected, reduced, projective scheme of dimension 1 over an algebraically closed field, admits two types
of compactifications of its (generalized) Jacobian: the moduli schemes of P-quasistable torsion-free, rank-1 sheaves and Seshadri’s moduli schemes of S-equivalence classes of semistable torsion-free,
rank-1 sheaves. Both are constructed with respect to a choice of polarization. The former are fine moduli spaces which were
shown to be complete; here we show that they are actually projective. The latter are just coarse moduli spaces. Here we give
a sufficient condition for when these two types of moduli spaces are equal.
Eduardo Esteves is Supported by CNPq, Processos 301117/04-7 and 470761/06-7, by CNPq/FAPERJ, Processo E-26/171.174/2003, and
by the Institut Mittag–Leffler (Djursholm, Sweden). 相似文献
9.
The ground-breaking research on the uniformization of curves was conducted at the beginning of the last century. Nevertheless,
there are few examples in the literature of algebraic curves for which an explicit uniformization is known. In this article
we obtain an explicit uniformization of the Fermat curves F
N
, for each
. The results presented here are based in part on an earlier study of the second author [6] in which each Riemann surface
F
N
(ℂ) was described as a quotient of the complex disk by a Fuchsian group Γ.
2000 Mathematics Subject Classification Primary—11F03, 11F06; Secondary—11F30
This work was partially supported by MCYT BFM2000-0627 and BMF2003-01898. 相似文献
10.
Áron Bereczky 《Journal of Mathematical Analysis and Applications》2005,304(2):607-613
Spectral synthesis on Abelian torsion groups is proved. 相似文献
11.
We note that three factors are missing from Table 1 in Factors of generalized Fermat numbers by A. Björn and H. Riesel published in Math. Comp. 67 (1998), 441-446.
12.
Numbers of the form are called Generalized Fermat Numbers (GFN). A computational method for testing the probable primality of a GFN is described which is as fast as testing a number of the form . The theoretical distributions of GFN primes, for fixed , are derived and compared to the actual distributions. The predictions are surprisingly accurate and can be used to support Bateman and Horn's quantitative form of ``Hypothesis H" of Schinzel and Sierpinski. A list of the current largest known GFN primes is included.
13.
Yerko Torres-Nova 《Journal of Pure and Applied Algebra》2021,225(1):106465
Let be integers. A generalized Fermat curve of type is a compact Riemann surface S that admits a subgroup of conformal automorphisms isomorphic to , such that the quotient surface is biholomorphic to the Riemann sphere and has branch points, each one of order k. There exists a good algebraic model for these objects, which makes them easier to study. Using tools from algebraic topology and integration theory on Riemann surfaces, we find a set of generators for the first homology group of a generalized Fermat curve. Finally, with this information, we find a set of generators for the period lattice of the associated Jacobian variety. 相似文献
14.
San Ling 《Proceedings of the American Mathematical Society》1998,126(11):3201-3210
For an integer and a prime not dividing , we study the kernel of the degeneracy map , where and are the component groups of and , respectively. This is then used to determine the kernel of the degeneracy map when . We also compute the group structure of in some cases.
15.
Julia Hartmann Anne V. Shepler 《Transactions of the American Mathematical Society》2008,360(1):123-133
Steinberg showed that when a finite reflection group acts on a real or complex vector space of finite dimension, the Jacobian determinant of a set of basic invariants factors into linear forms which define the reflecting hyperplanes. This result generalizes verbatim to fields whose characteristic is prime to the order of the group. Our main theorem gives a generalization of Steinberg's result for groups with a polynomial ring of invariants over arbitrary fields using a ramification formula of Benson and Crawley-Boevey.
16.
《Journal of Number Theory》2002,97(1):95-112
We examine densities of several sets connected with the Fermat numbers Fm=22m+1. In particular, we prove that the series of reciprocals of all prime divisors of Fermat numbers is convergent. We also show that the series of reciprocals of elite primes is convergent. 相似文献
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Constraint qualifications in terms of approximate Jacobians are investigated for a nonsmooth constrained optimization problem, in which the involved functions are continuous but not necessarily locally Lipschitz. New constraint qualifications in terms of approximate Jacobians, weaker than the generalized Robinson constraint qualification (GRCQ) in Jeyakumar and Yen [V. Jeyakumar, N.D. Yen, Solution stability of nonsmooth continuous systems with applications to cone-constrained optimization, SIAM J. Optim. 14 5 (2004) 1106-1127], are introduced and some examples are provided to show the utility of constrained qualifications introduced. Since the calmness condition is regarded as the basic condition for optimality conditions, the relationships between the constraint qualifications proposed and the calmness of solution mapping are also studied. 相似文献
19.
《数学的实践与认识》2015,(8)
对于正整数n,设F_n=2~2~n+1是第n个Fermat数,又设S(F_n)是F_n的Smarandache函数.运用初等的方法证明了:当n≥4时S(F_n)≥4·2~n(4n+9)+1. 相似文献
20.
《代数通讯》2013,41(10):5179-5189
Abstract Let I(X, F) denote the incidence algebra of the locally finite partially ordered set, X, defined over the field, F. This paper considers when the set of torsion elements of I(X, F) forms a group. If F is of finite characteristic, it is shown that the torsion elements of I(X, F) form a group if and only if X is bounded, while if F is of characteristic 0, the torsion elements of the incidence algebra form a group if and only if X is an antichain. 相似文献