Đề tài " The stable moduli space of Riemann surfaces: Mumford’s conjecture " ppt

... of Mathematics The stable moduli space of Riemann surfaces: Mumford’s conjecture By Ib Madsen and Michael Weiss* MUMFORD’S CONJECTURE 861 The stabilizer O(i, d +1− i)ofq i for the ... the source of π  ψ is the disjoint union of the sources of π and ψ. (See the remark just below.) To make the monoid structure explicit in the case of th...

Ngày tải lên: 06/03/2014, 08:21

... semistable, and, being both of degree 0, the sheaf E 1 is also of degree 0 and Mumford semistable. Note that E 1 is a solvable ideal of E, i.e. the fibers of E 1 are solvable ideals of the fibers of ... Section 1 the results in [G-S1] in order to construct the moduli space of g  -sheaves, then that of principal sheaves in Sections 2, 3 and 4. Recall, from the in...

Ngày tải lên: 16/02/2014, 05:20

... Part[n] is the set of partitions P of the set {1, ,n}. Here, (P )isthe length of the partition, and z P i denotes the variable set indexed by the part P i . The genus expansion for the disconnected ... expansion of the definition of A(µ i ,uµ i ), the Annals of Mathematics The equivariant Gromov- Witten theory of P1 By A. Okounkov and R. Pandharipand...

Ngày tải lên: 16/02/2014, 06:20

... image of F . For the details of these arguments we refer to Section 5 of [Sch]. Proof of the rigidity theorem. We use the same kind of argument as in the 2-local situation considered in [Sch]; the ... spectra, these two uses of ‘α 1 ∧ X’ are consistent. This finishes the proof of the rigidity theorem. Essentially the same proof as above proves the following some...

Ngày tải lên: 22/03/2014, 20:21

... convexity, J k is the maximizer of the entropy over B k and the minimizer of the 2-norm. By the same token, the permutation matrices are minimizers of the entropy and maximizers of the 2-norm. The constant c ... M k (R) the space of all k × k matrices over R and let F be the subspace of M k (R) consisting of all matrices X =(x ij ) for which the sum of...

Ngày tải lên: 29/03/2014, 07:20

... diameter of the union of the balls B c in s i (y i ). Namely, the balls B s i (y i ) are disjoint and satisfy the cone property (1) and, therefore, we get a bound for the sum of the radii s i of these balls  i s i ≤ ... a few of the results from [CM6] to be used. The first of these, Theorem 0.7 in [CM6], gives the existence of multi-valued graphs near a blow-up...

Ngày tải lên: 29/03/2014, 07:20

... 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 surface) of a strictly ... graph. (The existence of the curves σ 1 , γ 1 , γ 2 will be established in the next section.) First we need two lemmas. The first of these is the following: L...

Ngày tải lên: 14/02/2014, 17:20

... (For special cases of this argument, the reader can consult the proof of Lemma 5.2 of [A2] and the discussion at the end of Section 10 of [AC].) The terms in the expansion therefore vanish. The remaining ... formula. In the second paper [II], we established a key reduction in the proof of one of the global theorems. In this paper, we shall complete the proo...

Ngày tải lên: 05/03/2014, 23:20

... GRAPHICAL OFF THE AXIS 35 In this part, we prove Theorem I.0.8 when the surface is in a slab, illus- trating the key points (the full theorem, using the results of this part, will be proved ... curvature estimates since it is stable) is sandwiched between the two others. Hence its sector is also almost flat. The proof of the extension theorem is somewhat more complicated th...

Ngày tải lên: 14/03/2014, 22:20