Tài liệu Đề tài " Dynamics of SL2(R) over moduli space in genus two " ppt

... OK1×···×OKn.Annals of Mathematics Dynamics of SL2(R) over moduli space in genus two By Curtis T. McMullen* DYNAMICS OF SL2(R) OVER MODULI SPACE IN GENUS TWO 415equipped with ... By passing to a covering space of E ifnecessary, we can assume p∗(H1(X, Z)) = H1(E,Z); then the degree of ω is thedegree of p. DYNAMICS OF SL2(R) OVER MODULI SPACE IN GENUS TWO 419Theorem ... multiplication In this section we review the theory of real multiplication, and classifyeigenforms for Riemann surfaces of genus two. DYNAMICS OF SL2(R) OVER MODULI SPACE IN GENUS TWO 413An...

Tài liệu Đề tài " Moduli space of principal sheaves over projective varieties " pptx

... equivalent to that of the corresponding tensor. This is the key initial point of this article, allowing us to use in Section 1 the results in [G-S1] in orderto construct the moduli space of g-sheaves, ... of Ei. After ﬁxing the Chern classes of E and of the line bundles associated to the principal bundle P and characters of G, we obtain a projective moduli space of semistable principal G-sheaves.We ... amorphism f in the category of schemes, we denote by fanthe correspondingmorphism in the category of analytic spaces. Recall that the underlying set of Yanis the set of closed points of Y , and...

Tài liệu Đề tài " Pair correlation densities of inhomogeneous quadratic forms " pdf

... −111;0sj.4.12 Lemma.Γkis of finite index in SL(2, ) (12)2k.Proof. The subgroup Γθ2k⊂ Γkis of finite index in SL(2, )2kandthus also in SL(2,) (12)2k.434 JENS MARKLOF4.13. Remark. Note ... Theorem 1.4 in [27] on the equidistribution of translates of unipotent orbits. Because of thesimple structure of the Lie groups studied here, the proof of Theorem 5.7 isless involved than in the ... to SL(2, )2k.4.14. In this paper, we will be interested in the case of quadratic forms in twovariables, i.e., k =2. The corresponding theta sum (defined for general k in 4.5) reads thenΘf(τ,φ;...

Tài liệu Đề tài " Hypersurface complements, Milnor fibers and higher homotopy groups of arrangments " ppt

... ranks of the quotients of the lower central series of π1 of certain arrangements, in combinatorial terms. The LCS formula for pure braid groups was discoveredby Kohno, starting from his pioneering ... Hpassing through the origin.Moreover, in this case, the polar curve ΓH,being deﬁned by homogeneousequations, is a union of lines Ljpassing through the origin. For each such linewe choose ... from the fact that theπ1-chain complex of the universal cover is verydiﬃcult to describe, in general. As explained in the introduction, we have two results in this direction, at the I-adic...

Tài liệu Đề tài " Moduli spaces of surfaces and real structures " doc

... Therefore we conclude in thiscase that the conjugate of the surface Sbelongs to the irreducible subset of the moduli space containing S.We are now going to explain the construction of our examples:Let ... structure.Proof. Observe that since S is a classifying space for the fundamentalgroup of π1(S), then by the isotropic subspace theorem of [Cat3] the Albanesemapping of X maps onto a curve C(I)2 of ... Catanese,Onthe moduli spaces of surfaces of general type, J. DiﬀerentialGeom. 19 (1984) 483–515.[Cat2], Automorphisms of rational double points and moduli spaces of surfaces of general type,...

Tài liệu Đề tài " Hochschild cohomology of factors with property Γ " doc

... .4. Joint continuity in the ·2-normThere is an extensive literature on the topic of joint and separate con-tinuity of functions of two variables (see [3], [28] and the references therein)with ... y)isjointly continuous at (b, 0), and thus at (0,0) from above. Sinceφ(x, y)=ψ(xu∗,y), joint continuity of φ at (0,0) follows immediately.We now show joint continuity at a general point (a, ... construction of hyperﬁnite subfactors withspecial properties and a new inequality of Grothendieck type for multilinearmaps. We prove joint continuity in the ·2-norm of separately ultraweaklycontinuous...

Tài liệu Đề tài " Hausdorff dimension of the set of nonergodic directions " ppt

... 1.Density of primitive lattice points. The main obstacle in our approach tofinding lowerbounds on Hausdorff dimension is the absence of primitive latticepoints in certain regions of the plane. ... smallestclosed interval containing all the limits obtainable by applying Lemma 2.3 toa sequence beginning with w. Define E(λ):=∩Ejwhere Ejis the union of the intervals associated to slits in Vj.Itiseasily ... realize E(λ)asadecreasing intersection of compact sets Ej,each of which is a disjoint union of closed intervals. Let V denote the set of vectors that satisfy the hypothesis of Lemma 2.1. Henceforth,...

Tài liệu Đề tài " On the volume of the intersection of two Wiener sausages " ppt

... proof is a straightforward adaptation andgeneralization of the proof of Proposition 3 in [3]. We outline the main steps,while skipping the details.Step 1. One of the basic ingredients in the ... obtain dN/η copies of Sη,N:Sjη,N,j=1, ,dNη,(2.43)and each point of Rdis contained in exactly d copies.2. We are going to look at how often the two Brownian motions cross theslices of ... we proceed with the proof of Proposition 6(ii).Proof . Each reﬂection of an excursion beginning with an exit-point andending with an entrance-point costs a factor 2 in probability. On the eventCcτ,log...

Tài liệu Đề tài " Higher composition laws II: On cubic analogues of Gauss composition " ppt

... point stabilizers in GL2(Z) × GL3(Z) ×GL3(Z) of the elements in the space of 2 × 3 × 3 integer matrices. Just asstabilizers in GL2(Z) of integer points in the space of binary quadratic ... determine the stabilizers over Z of the other two spaces of formsindicated above, again in terms of the unit groups of orders in cubic ﬁelds.This article is organized as follows. Each of the ... orbits of these three spaces,and we describe the resulting groups in terms of ideal class groups of cubicrings. Finally, the work contained herein was motivated in part by staring atDynkin diagrams...

Tài liệu Đề tài " Geometry of the uniform spanning forest: Transitions in dimensions 4, 8, 12, . . . " pptx

... Zd.5. Proofs of main resultsProof of Theorem 1.1. Denote m = d−14. By applying Corollary 3.4to m + 1 independent copies of the USF relation, and invoking Theorems4.2 and 4.5, we infer that ... in E1and delet-ing the edges in E2. Let H be the graph obtained from Zdby contracting theedges in K1and deleting the edges in K2. By ﬁrst choosing ΥRand continuingwith Wilson’s ... (Domination). Let F, F0,F1,F2, ,Fmbe independentsamples of the wired USF in the graph G.LetC(x, F ) denote the vertex set of the component of x in F . Fix a distinguished vertex v0in...

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