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

... 2001) Annals of Mathematics Moduli spaces of surfaces and real structures By Fabrizio Catanese* Annals of Mathematics, 158 (2003), 577–592 Moduli spaces of surfaces and real structures By ... seminar, E. Klassen MODULI SPACES OF SURFACES AND REAL STRUCTURES 591 and V. Kharlamov for a useful conversation, V. Kulikov and Sandro M...

Ngày tải lên: 14/02/2014, 16:20

... R k and R  k,j ≥ R k,j . Similarly, each r x can be replaced by any r  x ≤ r x . This will be used freely in the proof of Theorem 0.1 below. Proof of Theorem 0.1. Let x k ,g k ,R k ,R k,j and ... curvature and area of stable sectors. A stable sector in the sense of [CM3], [CM4] is a stable subset of a minimal surface given as half of a normal tubular neighborhood (in the s...

Ngày tải lên: 14/02/2014, 17:20

... representation of G on the semisimple part g  of the Lie algebra of G, and ϕ is given by the Lie algebra structure. To obtain a projective moduli space we have to allow E to Annals of Mathematics Moduli ... the category of schemes, we denote by f an the corresponding morphism in the category of analytic spaces. Recall that the underlying set of Y an is the set of c...

Ngày tải lên: 16/02/2014, 05:20

... THE K 2 OF DEGENERATIONS OF SURFACES 343 We will often consider two particular kinds of trees T n : a chain R n of length n and the fork S n with n −1 teeth, i.e. a tree consisting of n −1 vertices joining ... cardinality of E, i.e. the number of irreducible components of double curves in X; • f n : the number of n-faces of G, i.e. the number of E n -points of X, f...

Ngày tải lên: 16/02/2014, 06:20

... natural action of SL 2 (R)onΩM 2 , the bundle of holomorphic 1-forms over the moduli space of Riemann surfaces of genus two. Contents 1. Introduction 2. Dynamics and Lie groups 3. Riemann surfaces and holomorphic ... stratum of Ω 1 M g has finite measure and finitely many components. Theorem 3.3. The action of SL 2 (R) is volume-preserving and ergodic on each component...

Ngày tải lên: 16/02/2014, 06:20

... is an arc b of ∂ 4 so that a push off γ  of a ∪ b lies in Q, misses a and separates the boundary components of Q into two sets of two, say one set is ∂ 1 and ∂ 2 and the other is ∂ 3 and ∂ 4 . ... III and S. T. Yau, The existence of embedded minimal surfaces and the problem of uniqueness, Math. Z. 179 (1982), 151–168. [15] ——— , The topological uniqueness of comple...

Ngày tải lên: 16/02/2014, 06:20

... is of index three in Γ k . Proof. It is well known [9] that Γ θ is of index three in SL(2, ) and SL(2, )= 2  j=0 Γ θ  0 −1 11  j . By virtue of the group isomorphism employed in the proof of ... measure of G k . This theorem is a special case of Shah’s more general Theorem 1.4 in [27] on the equidistribution of translates of unipotent orbits. Because of the simple struc...

Ngày tải lên: 14/02/2014, 16:20

... theory and degree of gradient maps The use of the local polar varieties in the study of singular spaces is already a classical subject; see Lˆe [Le1], Lˆe-Teissier [LT] and the references 482 ALEXANDRU ... there. Proof of Theorem 1. In view of Hamm’s affine Lefschetz theory, see [H, Th. 5], the only thing to prove is the equality between the number k n of n-cells attached and...

Ngày tải lên: 14/02/2014, 16:20

... 3.2.4 of [39] and the proof of Theorem 5.1 of [40] make it clear that ψ can be chosen to satisfy (6.22) ψ≤K k φ for some absolute constant K k . 656 E. CHRISTENSEN, F. POP, A. M. SINCLAIR, AND ... of a von Neumann factor M⊆B(H)oftypeII 1 with property Γ are zero for all positive integers k. The method of proof involves the construction of hyperfinite subfactors with special...

Ngày tải lên: 14/02/2014, 17:20

... proof. Proof of Theorem 4. Let α  and α  denote the left and right endpoints of I, respectively. Let q k be the largest height in Spec(α) ∩ [Q, R]. By (2), p k /q k ∈ I and without loss of ... 387–442. [MS] H. Masur and J. Smillie, Hausdorff dimension of sets of nonergodic measured folia- tions, Ann. of Math. 134 (1991), 455–543. [MT] H. Masur and S. Tabachnikov, Ratio...

Ngày tải lên: 14/02/2014, 17:20