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1.
LetX be a Riemann surface of genusg. The surfaceX is called elliptic-hyperelliptic if it admits a conformal involutionh such that the orbit spaceX/〈h〉 has genus one. The involutionh is then called an elliptic-hyperelliptic involution. Ifg>5 then the involutionh is unique, see [A]. We call symmetry to any anticonformal involution ofX. LetAut
±(X) be the group of conformal and anticonformal automorphisms ofX and letσ, τ be two symmetries ofX with fixed points and such that {σ, hσ} and {τ, hτ} are not conjugate inAut
±(X). We describe all the possible topological conjugacy classes of {σ, σh, τ, τh}. As consequence of our study we obtain that, in the moduli space of complex algebraic curves of genusg (g even >5), the subspace whose elements are the elliptic-hyperelliptic real algebraic curves is not connected. This fact contrasts
with the result in [Se]: the subspace whose elements are the hyperelliptic real algebraic curves is connected.
The authors are supported by BFM2002-04801. 相似文献
2.
Zoran Vondraček 《Probability Theory and Related Fields》1992,92(1):41-50
Summary LetX
h
be anh-Brownian motion in the unit ballDR
d
withh harmonic, such that the representing measure ofh is not singular with respect to the surface measure on D. IfY is a continuous strong Markov process inD with the same killing distributions asX
h
, thenY is a time change ofX
h
. Similar results hold in simply connected domains inC provided with either the Martin or the Euclidean boundary. 相似文献
3.
John Panaretos 《Annals of the Institute of Statistical Mathematics》1981,33(1):191-198
Summary LetX, Y be two discrete random variables with finite support andX≧Y. Suppose that the conditional distribution ofY givenX can be factorized in a certain way. This paper provides a method of deriving the unique form of the marginal distribution
ofX (and hence the joint distribution of (X, Y)) when partial independence only is assumed forY andX−Y. 相似文献
4.
R. Grant Woods 《Israel Journal of Mathematics》1971,9(2):250-256
We characterize the maximalm-bounded extension of an arbitrary completely regular Hausdorff spaceX. The other principal results are:Theorem. LetX be a locally compact, σ-compact non-compact space with no more than 2ℵ0 zero-sets. Then assuming the continuum hypothesis,βX − X can be written as the union of 22ℵ0 pairwise disjoint, dense ℵ0-bounded subspaces.Theorem. LetX be a locally compact, σ-compact metric space without isolated points. Then both the set of remote points ofβX and the complement of this set inβX −X are ℵ0-bounded. 相似文献
5.
LetX be a (not necessarily closed) subspace of the dual spaceB
*
of a separable Banach spaceB. LetX
1
denote the set of all weak
*
limits of sequences inX. DefineX
a
, for every ordinal numbera, by the inductive rule:X
a
= (U
b
<
a
X
b
)
1
.There is always a countable ordinala such thatX
a
is the weak
*
closure ofX; the first sucha is called theorder ofX inB
*
.
LetE be a closed subset of a locally compact abelian group. LetPM(E) be the set of pseudomeasures, andM(E) the set of measures, whose supports are contained inE. The setE obeys synthesis if and only ifM(E) is weak
*
dense inPM(E). Varopoulos constructed an example in which the order ofM(E) is 2. The authors construct, for every countable ordinala, a setE inR that obeys synthesis, and such that the order ofM(E) inPM(E) isa.
This work was done in Jerusalem, when the second-named author was a visitor at the Institute of Mathematics of the Hebrew
University of Jerusalem, with the support of an NSF International Travel Grant and of NSF Grant GP33583. 相似文献
6.
K. -H. Küfer 《Journal of Complexity》1996,12(4):339-357
Leta1, . . . ,ambe independent random points in
nthat are independent and identically distributed spherically symmetrical in
n. Moreover, letXbe the random polytope generated as the convex hull ofa1, . . . ,amand letLkbe an arbitraryk-dimensional subspace of
nwith 2 ≤k≤n− 1. LetXkbe the orthogonal projection image ofXinLk. We call those vertices ofXwhose projection images inLkare vertices ofXkshadow vertices ofXwith respect to the subspaceLk. We derive a distribution independent sharp upper bound for the expected number of shadow vertices ofXinLk. 相似文献
7.
LetX andY be infinite graphs such that the automorphism group ofX is nonamenable and the automorphism group ofY has an infinite orbit. We prove that there is no automorphism-invariant measure on the set of spanning trees in the direct
productX×Y. This implies that the minimal spanning forest corresponding to i.i.d. edge-weights in such a product has infinitely many
connected components almost surely.
Research partially supported by NSF grant DMS-9803597. 相似文献
8.
LetX be a locally compact non compact space. Necessary and sufficient conditions forfX/X to be a retract offX are given wherefX is the Freudenthal compactification ofX. LetX be a locally compact and zero dimensional space,m be any cardinal number andJ be a set with cardinalitym. It is proved thatX has a dyadic family of powerm if and only if there exist and compactificationY ofX such thatY/X=2 J andY/X is a retract ofY. 相似文献
9.
LetX andY be arbitrary non-empty sets and letS a non-empty subset ofX ×Y. We give necessary and sufficient conditions onS which ensure that every real valued function onS is the sum of a function onX and a function onY. 相似文献
10.
Friedrich Knop 《Mathematische Annalen》1993,295(1):333-363
Summary LetG be a reductive group defined over an algebraically closed fieldk and letX be aG-variety. In this paper we studyG-invariant valuationsv of the fieldK of rational functions onX. These objects are fundamental for the theory of equivariant completions ofX. LetB be a Borel subgroup andU the unipotent radical ofB. It is proved thatv is uniquely determined by its restriction toK
U
. Then we study the set of invariant valuations having some fixed restrictionv
0, toK
B
. Ifv
0 is geometric (i.e., induced by a prime divisor) then this set is a polyhedron in some vector space. In characteristic zero we prove that this polyhedron is a simplicial cone and in fact the fundamental domain of finite reflection groupW
X
. Thus, the classification of invariant valuations is almost reduced to the classification of valuations ofK
B
.
Unterstützt durch den Schweizerischen Nationalfonds zur Förderung der wissenschaftlichen Forschung. 相似文献
11.
G. T. Sallee 《Israel Journal of Mathematics》1976,24(3-4):368-376
LetK be a compact, convex subset ofE
dwhich can be tiled by a finite number of disjoint (on interiors) translates of some compact setY. Then we may writeK=X+Y, whereX is finite. The possible structures forK, X andY are completely determined under these conditions. 相似文献
12.
LetG be a reductive algebraic group and letH be a reductive subgroup ofG. We describe all pairs (G, H) such that, for any affineG-varietyX with a denseG-orbit isomorphic toG/H, the number ofG-orbits inX is finite.Work of both authors was supported by INTAS-OPEN-97-1570, by CRDF grant RM1-2088, and by RFBR grant 01-01-00756. 相似文献
13.
M. Valdivia 《Israel Journal of Mathematics》1987,59(1):107-111
LetX be a Banach space and letZ be a closed subspace ofX** which containsX. It is proved in this paper that, in the caseX** separable, there exists a closed subspaceY ofX such thatX+
=Z,
the closure ofY inX** for the weak-star topology. 相似文献
14.
Anna Di Concilio 《Monatshefte für Mathematik》1989,107(4):303-308
LetX be a completely regular space and 2
X
the hyperspace ofX. It is shown that the uniform topologies on 2
X
arising from Nachbin uniformity onX, which is the weak uniformity generated byC(X, ), and from Tukey—Shirota uniformity onX, generated by all countable open normal coverings ofX, agree. They, both, coincide with a Vietoris-type topology on 2
X
, the countable locally finite topology, iffX is normal. 相似文献
15.
Sergio Licanic 《Bulletin of the Brazilian Mathematical Society》2000,31(1):113-125
LetF be a holomorphic singular foliation with an invariant compact curveS on a compact algebraic surfaceX. In this work we prove thatF is logarithmic under some generic conditions in the singularities ofF inS.Supported by CNPq (Brazil). 相似文献
16.
Mladen Božiĉević 《manuscripta mathematica》1994,85(1):217-226
LetG be a complex semisimple Lie group,B its Borel subgroup andX a flag variety ofG. We define a functor on the category ofB-equivariantD
X-modules that corresponds, under the global section functor, to the Enright functor on the highest weight category. We use
this to lift Enright functor to the mixed version of the highest weight category. As an application we obtain that the socle
and the cosocle filtration of a primitive quotient of the enveloping algebra coincide. 相似文献
17.
Makoto Masumoto 《Israel Journal of Mathematics》2000,116(1):77-92
Leth be a homeomorphic bijection between hyperbolic Riemann surfacesR andR’. If there is a conformal mapping ofR intoR’ homotopic toh, then for any hyperbolic geodesicc onR the length of the hyperbolic geodesic freely homotopic to the imageh(c) is less than or equal to the hyperbolic length ofc. We show that the converse is not necessarily true. 相似文献
18.
Ruzong Fan 《应用数学学报(英文版)》1992,8(2):153-167
LetB be a separable real Banach space andX(t) be a symmetric conservative diffusion process taking values inB. In this paper, we decompose the functionalu(X(t),t) into a sum of a square integrable martingale and a regular 0-quadratic variation process. On this basis, we establish the predictable representation theorem ofX(t).This project is supported by the National Natural Science Foundation of China. 相似文献
19.
LetA be an abelian variety defined over a number fieldK. LetL be a finite Galois extension ofK with Galois groupG and let III(A/K) and III(A/L) denote, respectively, the Tate-Shafarevich groups ofA overK and ofA overL. Assuming these groups are finite, we compute [III(A/L)
G
]/[III(A/K)] and [III(A/K)]/[N(III(A/L))], where [X] is the order of a finite abelian groupX. Especially, whenL is a quadratic extension ofK, we derive a simple formula relating [III(A/L)], [III(A/K)], and [III(A
x/K)] whereA
x is the twist ofA by the non-trivial characterχ ofG. 相似文献