Đề tài " Geometrization of 3dimensional orbifolds " pot

... extensive use of the letter Σ, namely for the singular locus of an orbifold. GEOMETRIZATION OF 3-DIMENSIONAL ORBIFOLDS 205 Example 3.2 (Geometric orbifolds) . A geometric orbifold of dimension ... quotient of the model space M n k by a finite group of isometries. Unlike topological orbifolds, geometric orbifolds are always global quo- tients, i.e. they are (even finite) quot...

Ngày tải lên: 15/03/2014, 09:20

... and the hypothesis holds for all T ’s verifying K ⊂ 4T , then the assertion holds for any T . Proof. The argument consists of two parts. The first part is essentially a copy of the proof of Lemma ... secondly [T], which demonstrates a form of duality involving some measures of the size of entire sequences (e k (u)), (e k (u ∗ )). The proof of the theorem consists of three parts...

Ngày tải lên: 14/03/2014, 22:20

... exactly 2 t h K of them (t = the number of primes dividing N , h K = class number of K), that 910 KARTIK PRASANNA split up into 2 t conjugacy classes under the action of the class group of K. (See ... E i i.e. a generator of the rank−1 Z-module H 0 (E i , Ω 1 ) where E i denotes the Neron model of E i over spec Z.IfA 2 is the INTEGRALITY OF A RATIO OF PETERSSON NORMS 911 ker...

Ngày tải lên: 06/03/2014, 08:21

... the range of the temporal distance function has zero lower box counting dimension. (See also [14] and [17, Th. 9.3].) Proof of Theorem 1.6(b). We only have to show that the hypotheses of Lemma ... E(Ψ 0 ,f) =0. The proof of (2  ) is particularly simple as f can be chosen to be supported in a small neighborhood of x H so that A N (Ψ 0 ,f)=f(p N ) − f(x H ). For the proof of (1 ...

Ngày tải lên: 15/03/2014, 09:20

... spontaneous appearance of a singularity in the shape of an evolving vortex sheet, Proc. R. Soc. London A 365 (1979), 105-119. [10] A. Morlet , Further properties of a continuum of model equations ... operator of ω. If we take an x derivative of (1.1) and define θ x ≡ ω we obtain a vis- cous version of the equation (1.3) with v = −Hθ which is similar to the one proposed in [6] and...

Ngày tải lên: 29/03/2014, 07:20

... clearly unaffected by the removal of D from Z d . 5. Proofs of main results Proof of Theorem 1.1. Denote m =  d−1 4 . By applying Corollary 3.4 to m + 1 independent copies of the USF relation, and invoking ... allow for future applications. The bulk of the paper is devoted to the proof of the upper bound on max N(x, y) in (1.1). We now present an overview of this proof. Let U (...

Ngày tải lên: 14/02/2014, 17:20

... classification of Q-systems up to equivalence when a system of endomorphisms is given and ρ is a direct sum of endomorphisms in the system. 2.5. Classification of local extensions of the SU(2) k net. ... desired. Remark 2.5. The proof of uniqueness for the E 8 case in [41, Sec. 6] uses vertex operator algebras. Izumi has recently given a direct proof of uniquenss of the Q-system...

Ngày tải lên: 14/02/2014, 17:20

... make use of this fact in the proof of Lemma 4.1. 4. Proof of the Main Lemma For any n ≥ n 0 , let k be such that c s n ∈ I m(k) −I m(k+1) , and let b n be an endpoint of I m(k+1)−1 . Recall that A n = |b n |  −|c s n+1 |  |b n |  −|c s n |  ,B n =  |c s n | |c s n+1 |  /2 . The ... an alternative proof of this result, using the method of “asymptotically conformal extension”...

Ngày tải lên: 16/02/2014, 05:20

... of orbifolds; the fiber over X ∈ Mod g is the space Ω(X) −{0}/ Aut(X). For brevity, we refer to (X, ω) ∈ ΩM g as a form of genus g. Action of GL + 2 (R). The group GL + 2 (R) of automorphism of ... or the complement of the spine of F ρ in X is a finite union of cylinders A 1 , ,A n . Moduli space. Let M g = T g / Mod g denote the moduli space of compact Riemann surfaces X of...

Ngày tải lên: 16/02/2014, 06:20

... The sheaf π ∗ (D  X ) T,η of sec- tions of π ∗ (D  X ) which transform by the character η under the action of T carries the structure of such a module. 3. Localization of g-modules to D-modules ... subscheme of  g ∗ ). We let N⊂g ∗ denote the nilpotent cone, i.e. the zero set of invariant polynomials of positive degree. 3.1.2. Restrictions on the characteristic p. Let h be...

Ngày tải lên: 16/02/2014, 06:20