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1.
Parabolic Raynaud bundles 总被引:1,自引:0,他引:1
Let X be an irreducible smooth projective curve defined over the field of complex numbers, a finite set of closed points and N ≥ 2 a fixed integer. For any pair , there exists a parabolic vector bundle on X, with parabolic structure over S and all parabolic weights in , that has the following property: Take any parabolic vector bundle of rank r on X whose parabolic points are contained in S, all the parabolic weights are in and the parabolic degree is d. Then is parabolically semistable if and only if there is no nonzero parabolic homomorphism from to . 相似文献
2.
Álvaro Lozano-Robledo 《manuscripta mathematica》2008,126(3):393-407
Let S be an infinite set of rational primes and, for some p ∈ S, let be the compositum of all extensions unramified outside S of the form , for . If , let be the intersection of the fixed fields by , for i = 1, . . , n. We provide a wide family of elliptic curves such that the rank of is infinite for all n ≥ 0 and all , subject to the parity conjecture. Similarly, let be a polarized abelian variety, let K be a quadratic number field fixed by , let S be an infinite set of primes of and let be the maximal abelian p-elementary extension of K unramified outside primes of K lying over S and dihedral over . We show that, under certain hypotheses, the -corank of sel
p
∞(A/F) is unbounded over finite extensions F/K contained in . As a consequence, we prove a strengthened version of a conjecture of M. Larsen in a large number of cases. 相似文献
3.
Let G be a finite group, an absolutely irreducible -module and w a weight of . To any Galois covering with group G we associate two correspondences, the Schur and the Kanev correspondence. We work out their relation and compute their invariants.
Using this, we give some new examples of Prym–Tyurin varieties.
This work was supported by FONDECYT No. 11060468 and No. 1060742. 相似文献
4.
Romyar T. Sharifi 《Mathematische Annalen》2008,342(2):297-308
Let p be an odd prime satisfying Vandiver’s conjecture. We consider two objects, the Galois group X of the maximal unramified abelian pro-p extension of the compositum of all Z
p
-extensions of Q(μ
p
) and the Galois group of the maximal unramified pro-p extension of Q
. We give a lower bound for the height of the annihilator of X as an Iwasawa module. Under some mild assumptions on Bernoulli numbers, we provide a necessary and sufficient condition for
to be abelian. The bound and the condition in the two results are given in terms of special values of a cup product pairing
on cyclotomic p-units. We obtain in particular that, for p < 1,000, Greenberg’s conjecture that X is pseudo-null holds and is in fact abelian. 相似文献
5.
Soogil Seo 《manuscripta mathematica》2008,127(3):381-396
A circular distribution is a Galois equivariant map ψ from the roots of unity μ
∞ to an algebraic closure of such that ψ satisfies product conditions, for ϵ ∈ μ
∞ and , and congruence conditions for each prime number l and with (l, s) = 1, modulo primes over l for all , where μ
l
and μ
s
denote respectively the sets of lth and sth roots of unity. For such ψ, let be the group generated over by and let be , where U
s
denotes the global units of . We give formulas for the indices and of and inside the circular numbers P
s
and units C
s
of Sinnott over .
This work was supported by the SRC Program of Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government
(MOST) (No. R11-2007-035-01001-0). This work was supported by the Korea Research Foundation Grant funded by the Korean Government
(MOEHRD, Basic Research Promotion Fund) (KRF-2006-312-C00455). 相似文献
6.
Finite groups with minimal 1-PIM 总被引:1,自引:0,他引:1
Let be a field of characteristic and let G be a finite group. It is well-known that the dimension of the minimal projective cover (the so-called 1-PIM) of the trivial left -module is a multiple of the -part of the order of G. In this note we study finite groups G satisfying . In particular, we classify the non-abelian finite simple groups G and primes satisfying this identity (Theorem A). As a consequence we show that finite soluble groups are precisely those finite groups
which satisfy this identity for all prime numbers (Corollary B). Another consequence is the fact that the validity of this identity for a finite group G and for a small prime number implies the existence of an -Hall subgroup for G (Theorem C). An important tool in our proofs is the super-multiplicativity of the dimension of the 1-PIM over short exact
sequences (Proposition 2.2). 相似文献
7.
Let be open, let be the Dirac operator in and let be the Clifford algebra constructed over the quadratic space . If for fixed, denotes the space of r-vectors in , then an -valued smooth function W = W
r
+ W
r+2 in Ω is said to satisfy the Moisil-Théodoresco system if . In terms of differential forms, this means that the corresponding - valued smooth form w = w
r
+ w
r+2 satisfies in Ω the system d
*
w
r
= 0, dw
r
+ d
*
w
r+2 = 0; dw
r+2 = 0.
Based on techniques and results concerning conjugate harmonic functions in the framework of Clifford analysis, a structure
theorem is proved for the solutions of the Moisil-Théodoresco system.
相似文献
8.
Let be a field, and M and N two finitely generated graded modules over standard graded -algebras A and B, respectively. We will study generalized, sequentially, almost, and approximately Cohen–Macaulay as well as clean, and pretty
clean properties of the -module through the corresponding properties of M and N. The behavior of these properties with respect to the simplicial join of two simplicial (multi)complexes will be revealed
as corollaries. 相似文献
9.
We study several deformation functors associated to the normalization of a reduced curve singularity . The main new results are explicit formulas, in terms of classical invariants of (X, 0), for the cotangent cohomology groups T
i
, i = 0,1,2, of these functors. Thus we obtain precise statements about smoothness and dimension of the corresponding local
moduli spaces. We apply the results to obtain explicit formulas, respectively, estimates for the -codimension of a parametrized curve singularity, where denotes the Mather–Wall group of left-right equivalence. 相似文献
10.
Let Λ be an algebraic set and let (n is even) be a polynomial mapping such that for each there is r(λ) > 0 such that the mapping g
λ = g(· , λ) restricted to the sphere S
n
(r) is an immersion for every 0 < r < r (λ), so that the intersection number I(g
λ|S
n
(r)) is defined. Then is an algebraically constructible function.
I. Karolkiewicz and A. Nowel supported by the grant BW/5100-5-0286-7. 相似文献
11.
Domenico Mucci 《manuscripta mathematica》2009,128(4):421-441
We deal with strong density results of smooth maps between two manifolds and in the fractional spaces given by the traces of Sobolev maps in W
1,p
. 相似文献
12.
Alexander Prestel 《manuscripta mathematica》2007,123(1):95-103
Let K be an algebraically closed field with a valuation ring or a real closed field with a convex valuation ring . We show that the projection of a basic (see “Introduction”) subset of to K
n
is again basic. 相似文献
13.
Jorge Antezana Enrique Pujals Demetrio Stojanoff 《Integral Equations and Operator Theory》2008,62(4):465-488
Let λ ∈ (0, 1) and let T be a r × r complex matrix with polar decomposition T = U|T|. Then the λ-Aluthge transform is defined by
. Let denote the n-times iterated Aluthge transform of T, . We prove that the sequence converges for every r × r diagonalizable matrix T. We show regularity results for the two parameter map , and we study for which matrices the map is constant.
The first and third author were partially supported by CONICET (PIP 4463/96), Universidad
de La Plata (UNLP 11 X472) and ANPCYT (PICT03-09521). The second author was partially
supported by CNPq. 相似文献
14.
F. Bastianelli 《manuscripta mathematica》2009,130(1):113-120
Let C be a very general curve of genus g and let C
(2) be its second symmetric product. This paper concerns the problem of describing the convex cone of all numerically effective -divisors classes in the Néron–Severi space . In a recent work, Julius Ross improved the bounds on in the case of genus five. By using his techniques and by studying the gonality of the curves lying on C
(2), we give new bounds on the nef cone of C
(2) when C is a very general curve of genus 5 ≤ g ≤ 8.
This work has been partially supported by (1) PRIN 2007 “Spazi di moduli e teorie di Lie”; (2) Indam (GNSAGA); (3) FAR 2008 (PV) “Varietá algebriche, calcolo algebrico, grafi orientati e topologici”. 相似文献
15.
We compute the and monodromy of every irreducible component of the moduli spaces of hyperelliptic and trielliptic curves. In particular, we
provide a proof that the monodromy of the moduli space of hyperelliptic curves of genus g is the symplectic group . We prove that the monodromy of the moduli space of trielliptic curves with signature (r,s) is the special unitary group .
Rachel Pries was partially supported by NSF grant DMS-04-00461. 相似文献
16.
David G. Wagner 《Annals of Combinatorics》2008,12(2):211-239
Mason’s Conjecture asserts that for an m-element rank r matroid the sequence is logarithmically concave, in which I
k is the number of independent k-sets of . A related conjecture in probability theory implies these inequalities provided that the set of independent sets of satisfies a strong negative correlation property we call the Rayleigh condition. This condition is known to hold for the set of bases of a regular matroid. We show that if ω is a weight function on a set
system that satisfies the Rayleigh condition then is a convex delta-matroid and ω is logarithmically submodular. Thus, the hypothesis of the probabilistic conjecture leads
inevitably to matroid theory. We also show that two-sums of matroids preserve the Rayleigh condition in four distinct senses,
and hence that the Potts model of an iterated two-sums of uniform matroids satisfies the Rayleigh condition. Numerous conjectures
and auxiliary results are included.
Research supported by the Natural Sciences and Engineering Research Council of Canada under operating grant OGP0105392. 相似文献
17.
Juha Lehrbäck 《manuscripta mathematica》2008,127(2):249-273
We establish necessary and sufficient conditions for a domain to admit the (p, β)-Hardy inequality , where d(x) = dist(x, ∂Ω) and . Our necessary conditions show that a certain dichotomy holds, even locally, for the dimension of the complement Ω
c
when Ω admits a Hardy inequality, whereas our sufficient conditions can be applied in numerous situations where at least
a part of the boundary ∂Ω is “thin”, contrary to previously known conditions where ∂Ω or Ω
c
was always assumed to be “thick” in a uniform way. There is also a nice interplay between these different conditions that
we try to point out by giving various examples.
The author was supported in part by the Academy of Finland. 相似文献
18.
Wenbin Guo 《manuscripta mathematica》2008,127(2):139-150
Let G be a finite group and a formation of finite groups. We say that a subgroup H of G is -supplemented in G if there exists a subgroup T of G such that G = TH and is contained in the -hypercenter of G/H
G
. In this paper, we use -supplemented subgroups to study the structure of finite groups. A series of previously known results are unified and generalized.
Research of the author is supported by a NNSF grant of China (Grant #10771180). 相似文献
19.
Nicola Garofalo 《manuscripta mathematica》2008,126(3):353-373
We prove some new a priori estimates for H
2-convex functions which are zero on the boundary of a bounded smooth domain Ω in a Carnot group . Such estimates are global and are geometric in nature as they involve the horizontal mean curvature of ∂Ω. As a consequence of our bounds we show that if has step two, then for any smooth H
2-convex function in vanishing on ∂Ω one has
.
Supported in part by NSF Grant DMS-07010001. 相似文献
20.
We present a method for computing pth roots using a polynomial basis over finite fields of odd characteristic p, p ≥ 5, by taking advantage of a binomial reduction polynomial. For a finite field extension of our method requires p − 1 scalar multiplications of elements in by elements in . In addition, our method requires at most additions in the extension field. In certain cases, these additions are not required. If z is a root of the irreducible reduction polynomial, then the number of terms in the polynomial basis expansion of z
1/p
, defined as the Hamming weight of z
1/p
or , is directly related to the computational cost of the pth root computation. Using trinomials in characteristic 3, Ahmadi et al. (Discrete Appl Math 155:260–270, 2007) give is greater than 1 in nearly all cases. Using a binomial reduction polynomial over odd characteristic p, p ≥ 5, we find always.
相似文献