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1.
Let M Rn be a connected component of an algebraic set 1(0),where is a polynomial of degree d. Assume that M is containedin a ball of radius r. We prove that the geodesic diameter ofM is bounded by 2rv(n)d(4d5)n2, where v(n) =(1/2)((n+1)/2)(n/2)1.This estimate is based on the bound rv(n)d(4d5)n2for the length of the gradient trajectories of a linear projectionrestricted to M. 2000 Mathematics Subject Classification 32Bxx,34Cxx (primary), 32Sxx, 14P10 (secondary). 相似文献
2.
Throughout this paper k denotes a fixed commutative ground ring.A CohenMacaulay complex is a finite simplicial complexsatisfying a certain homological vanishing condition. Thesecomplexes have been the subject of much research; introductionscan be found in, for example, Björner, Garsia and Stanley[6] or Budach, Graw, Meinel and Waack [7]. It is known (see,for example, Cibils [8], Gerstenhaber and Schack [10]) thatthere is a strong connection between the (co)homology of anarbitrary simplicial complex and that of its incidence algebra.We show how the CohenMacaulay property fits into thispicture, establishing the following characterization. A pure finite simplicial complex is CohenMacaulay overk if and only if the incidence algebra over k of its augmentedface poset, graded in the obvious way by chain lengths, is aKoszul ring. 相似文献
3.
An index of a collection of 1-forms on a complex isolated completeintersection singularity corresponding to a Chern number isdefined and in the case when the 1-forms are complexanalytic expressed as the dimension of a certain algebra.2000 Mathematics Subject Classification 32S50, 57R20, 57R25. 相似文献
4.
The purpose of this paper is to show how the methods of motivicintegration of Kontsevich, DenefLoeser (Invent. Math.135 (1999) 201232 and Compositio Math. 131 (2002) 267290)and Looijenga (Astérisque 276 (2002) 267297) canbe adapted to prove the McKayRuan correspondence, a generalizationof the McKayReid correspondence to orbifolds that arenot necessarily global quotients. 2000 Mathematics Subject Classification14A20, 14E15, 14F43. 相似文献
5.
6.
We describe a method for constructing explicit algebraic solutionsto the sixth Painlevé equation, generalising that ofDubrovin and Mazzocco. There are basically two steps. Firstwe explain how to construct finite braid group orbits of triplesof elements of SL2(C) out of triples of generators of three-dimensionalcomplex reflection groups. (This involves the FourierLaplacetransform for certain irregular connections.) Then we adapta result of Jimbo to produce the Painlevé VI solutions.(In particular, this solves a RiemannHilbert problemexplicitly.) Each step is illustrated using the complex reflection groupassociated to Klein's simple group of order 168. This leadsto a new algebraic solution with seven branches. We also provethat, unlike the algebraic solutions of Dubrovin and Mazzoccoand Hitchin, this solution is not equivalent to any solutioncoming from a finite subgroup of SL2(C). The results of this paper also yield a simple proof of a recenttheorem of Inaba, Iwasaki and Saito on the action of Okamoto'saffine D4 symmetry group as well as the correct connection formulaefor generic Painlevé VI equations. 2000 Mathematics SubjectClassification 34M55, 34M40, 20F55. 相似文献
7.
In this paper we determine the possible Hilbert functions ofa CohenMacaulay local ring of dimension d and multiplicitye, in the case where the embedding dimension v satisfies v =e + d 3 and the CohenMacaulay type is less thanor equal to e 3. 1991 Mathematics Subject Classification:primary 13D40; secondary 13P99. 相似文献
8.
Let Pf(x) = if'(x) and Qf(x) = xf(x) be the canonicaloperators acting on an appropriate common dense domain in L2(R).The derivations DP(A) = i(PAAP) and DQ(A) = i(QAAQ)act on the *-algebra A of all integral operators having smoothkernels of compact support, for example, and one may considerthe noncommutative Laplacian, L = + , as a linear mapping of A into itself. L generates a semigroup of normal completely positive linearmaps on B(L2(R)), and this paper establishes some basic propertiesof this semigroup and its minimal dilation to an E0-semigroup.In particular, the author shows that its minimal dilation ispure and has no normal invariant states, and he discusses thesignificance of those facts for the interaction theory introducedin a previous paper. There are similar results for the canonical commutation relationswith n degrees of freedom, where 1 n < . 2000 MathematicsSubject Classification 46L57 (primary), 46L53, 46L65 (secondary). 相似文献
9.
Satisfactory error estimates are obtained from iterative refinementof the solution using Ml, an approximation to the inverseof A and involving ||IM1A||. 相似文献
10.
This paper investigates how to relate the syzygy periodicityof a self-injective algebra A to its AuslanderReitenperiodicity. Moreover, a characterization is provided of theAuslanderReiten bounded AA-bimodules that areperiodic. 2000 Mathematics Subject Classification 16G70, 16E40(primary), 16G20 (secondary). 相似文献
11.
Guerrero Julio Becerra; Rodriguez-Palacios Angel; Wood Geoffrey V. 《Bulletin London Mathematical Society》2003,35(2):218-224
An element u of a norm-unital Banach algebra A is said to beunitary if u is invertible in A and satisfies ||u|| = ||u1||= 1. The norm-unital Banach algebra A is called unitary if theconvex hull of the set of its unitary elements is norm-densein the closed unit ball of A. If X is a complex Hilbert space,then the algebra BL(X) of all bounded linear operators on Xis unitary by the RussoDye theorem. The question of whetherthis property characterizes complex Hilbert spaces among complexBanach spaces seems to be open. Some partial affirmative answersto this question are proved here. In particular, a complex Banachspace X is a Hilbert space if (and only if) BL(X) is unitaryand, for Y equal to X, X* or X** there exists a biholomorphicautomorphism of the open unit ball of Y that cannot be extendedto a surjective linear isometry on Y. 2000 Mathematics SubjectClassification 46B04, 46B10, 46B20. 相似文献
12.
A Step Beyond Kneser's Theorem for Abelian Finite Groups 总被引:1,自引:0,他引:1
13.
Let C be a genus 2 algebraic curve defined by an equation ofthe form y2 = x(x2 1)(x a)(x 1/a). Asis well known, the five accessory parameters for such an equationcan all be expressed in terms of a and the accessory parameter b corresponding to a. The main result of the paper is thatif a' = 1 a2, which in general yields a non-isomorphiccurve C', then b'a'(a'2 1) = ba(a2 1). This is proven by it being shown how the uniformizing functionfrom the unit disk to C' can be explicitly described in termsof the uniformizing function for C. 相似文献
14.
The existence of periodic solutions for the nonlinear asymmetricoscillator x' + x+ rßx = h(t),(' =d/dt (is discussed, where , rß are positive constantssatisfying for some positive integer n N and h(t) L (0,2) is 2-periodic with x±= max {±x,0}. 2000 Mathematics Subject Classification34C10, 34C25. 相似文献
15.
Let be a conjugation, alias a conjugate linear isometry oforder 2, on a complex Banach space X and let X be the real formof X of -fixed points. In contrast to the DunfordPettisproperty, the alternative DunfordPettis property neednot lift from X to X. If X is a C*-algebra it is shown thatX has the alternative DunfordPettis property if and onlyif X does and an analogous result is shown when X is the dualspace of a C*-algebra. One consequence is that both DunfordPettisproperties coincide on all real forms of C*-algebras. 相似文献
16.
Alekseevsky Dmitri V.; Di Scala Antonio J. 《Proceedings London Mathematical Society》2004,89(1):193-216
We study the (restricted) holonomy group Hol() of the normalconnection (shortened to normal holonomy group) of a Kählersubmanifold of a complex space form. We prove that if the normalholonomy group acts irreducibly on the normal space then itis linear isomorphic to the holonomy group of an irreducibleHermitian symmetric space. In particular, it is a compact groupand the complex structure J belongs to its Lie algebra. We prove that the normal holonomy group acts irreducibly ifthe submanifold is full (that is, it is not contained in a totallygeodesic proper Kähler submanifold) and the second fundamentalform at some point has no kernel. For example, a KählerEinsteinsubmanifold of CPn has this property. We define a new invariant µ of a Kähler submanifoldof a complex space form. For non-full submanifolds, the invariantµ measures the deviation of J from belonging to the normalholonomy algebra. For a KählerEinstein submanifold,the invariant µ is a rational function of the Einsteinconstant. By using the invariant µ, we prove that thenormal holonomy group of a not necessarily full KählerEinsteinsubmanifold of CPn is compact, and we give a list of possibleholonomy groups. The approach is based on a definition of the holonomy algebrahol(P) of an arbitrary curvature tensor field P on a vectorbundle with a connection and on a De Rham type decompositiontheorem for hol(P). 2000 Mathematics Subject Classification53C40 (primary), 53B25 (secondary). 相似文献
17.
It is proved that the infinitesimal generator A of a stronglycontinuous semigroup of linear operators on a Hilbert spacealso generates a strongly continuous group if and only if theresolvent of A, ( + A)1, is also a bounded functionon some right-hand-side half plane of complex numbers, and convergesstrongly to zero as the real part of tends to infinity. Anapplication to a partial differential equation is given. 1991Mathematics Subject Classification 47D03. 相似文献
18.
The structural stability of constrained polynomial differentialsystems of the form a(x, y)x'+b(x, y)y'=f(x, y), c(x, y)x'+d(x,y)y'=g(x, y), under small perturbations of the coefficientsof the polynomial functions a, b, c, d, f and g is studied.These systems differ from ordinary differential equations atimpasse points defined by adbc=0. Extensionsto this case of results for smooth constrained differentialsystems [7] and for ordinary polynomial differential systems[5] are achieved here. 1991 Mathematics Subject Classification34C35, 34D30. 相似文献
19.
Let H be the IwahoriHecke algebra associated with Sn,the symmetric group on n symbols. This algebra has two importantbases: the KazhdanLusztig basis and the Murphy basis.We establish a precise connection between the two bases, allowingus to give, for the first time, purely algebraic proofs fora number of fundamental properties of the KazhdanLusztigbasis and Lusztig's results on the a-function. 2000 MathematicsSubject Classification 20C08. 相似文献
20.
Given an affine domain of GelfandKirillov dimension 2over an algebraically closed field, it is shown that the centralizerof any non-scalar element of this domain is a commutative domainof GelfandKirillov dimension 1 whenever the domain isnot polynomial identity. It is shown that the maximal subfieldsof the quotient division ring of a finitely graded Goldie algebraof GelfandKirillov dimension 2 over a field F all havetranscendence degree 1 over F. Finally, centralizers of elementsin a finitely graded Goldie domain of GelfandKirillovdimension 2 over an algebraically closed field are considered.In this case, it is shown that the centralizer of a non-scalarelement is an affine commutative domain of GelfandKirillovdimension 1. 2000 Mathematics Subject Classification 16P90. 相似文献