Tài liệu Đề tài " On the K2 of degenerations of surfaces and the multiple point formula " pptx

... which is the composition of blow-ups at points of the central fibre, such that X  is smooth. Annals of Mathematics On the K2 of degenerations of surfaces and the multiple point formula ... component of type (i), then the intersection in codimension one of any two distinct components can only be a line. If there is no component of type (i), then t...

Ngày tải lên: 16/02/2014, 06:20

... second term on the right-hand side of the analogue of (2.93). 4. Proof of Theorem 3 In Sections 4–6 we prove Theorems 3–5. The proof follows the same line of reasoning as in [3, §5], but there ... N-boxes), and therefore the estimate in (2.63) implies that most of the intersection volume is unaffected by the reflections. 8. Before giving the proof of Propositions...

Ngày tải lên: 14/02/2014, 17:20

... for the size of the neighbourhood V of the singular set on noncontracted components is the diameter of ϕ(V )inM; on contracted components one may take the smallest ε with V contained in the ε-thin ... if and only if |C| is smooth and m(C) = 0 if and only if C has no multiple components. The definition of the C 0 -topology on the space of pseudo-holomor...

Ngày tải lên: 16/02/2014, 05:20

... to the proof of Theorem 5. Keep the notation and the assumptions of this theorem. Assume that the parameter w>1 is fixed, as well as the sequences (U n ) n≥1 and (V n ) n≥1 occurring in the ... get, on the one hand, that |U n | |V n | ≤ |W 1 | 1+|W 2 | ≤ r − 1 and, on the other hand, that σ n (u) is a prefix of V n of length at least 1/r times the length o...

Ngày tải lên: 16/02/2014, 06:20

... Diophantine. The construction of this Cantor set is based on Lemma 1.1 and is presented in Section 2. The proof of Theorem 2 is completed in Section 3 if we assume the statement of Theorem 3, whose proof ... integer satisfies the hypothesis of Theorem 1. Some generalizations of Theorem 1 are mentioned in Section 2. For the class of Veech billiards (see [V2]) the set...

Ngày tải lên: 14/02/2014, 17:20

... HIGHER COMPOSITION LAWS II 873 The proof of Theorem 2 not only gives a complete description of the nondegenerate orbits of the representation of Γ on Z 2 ⊗ Z 3 ⊗ Z 3 in terms of cubic rings, ... of Sections 2.3 and 3.1. As shown in Section 2.3, the GL 2 factor of L acts on the basis of a cubic ring R, while the two SL 3 factors act on the bases of two i...

Ngày tải lên: 14/02/2014, 17:20

... further condition on the occurrence of S, then we should also contract the edges in K 1 and delete the edges in K 2 . Therefore, conditionally on Υ R and the occurrence of S, the path γ R has the distribution ... be the USF on Z d , and denote by Γ D the event that there are no oriented edges in F from D c to D. Then the distribution of F ∩  D c conditione...

Ngày tải lên: 14/02/2014, 17:20

... ˜σ 1 | [a,b] is noncontractible, then we are done. Otherwise, if ˜σ 1 | [a,b] bounds a disk, then we apply the Gauss-Bonnet theorem to see that ˜σ 1 | (a,b) contains a break and proceed as in the proof of ... .(II.1.14) Proof. Following the first two steps of the proof of Lemma II.1.11 (with the obvious modifications), we get a simple closed broken geodesic ˜σ 1 which is nonco...

Ngày tải lên: 14/02/2014, 17:20

... ∈ Ξ i (C d i ) ∩F κ then Ξ i (C d i )=J i+1 [g]. We will concentrate on the analysis of the regularity of Ξ i for the spe- cial class of simple maps f: one of the good properties of the class of simple maps ... describe the general strategy behind the proofs of Theorems A and B. (1) We consider a certain set of nonregular parameters of full measure and de...

Ngày tải lên: 16/02/2014, 05:20