Tài liệu Đề tài "Gr¨obner geometry of Schubert polynomials " ppt

... Cohen–Macaulayness of the initial scheme L w as part of our evidence for the naturality of Gr¨obner geometry for Schubert polynomials, and the generality of subword complexes allows our simple proof of their ... multidegree of X equals the sum of multidegrees of components of Y that happen also to be compo- nents of X. By hypothesis, the multidegrees of X and Y coin...

Ngày tải lên: 16/02/2014, 05:20

... 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 ... an GEOMETRY OF THE UNIFORM SPANNING FOREST 477 arbitrary ordering of the vertices of a transient graph G. Let X 1 be a simple random walk started from v 1 . Let F 1 den...

Ngày tải lên: 14/02/2014, 17:20

... 12.2 of [13]. We note that these proofs of the starting condition make elaborate use of “complex” methods and do not seem to work for the case <2. In this paper, we shall prove the decay of geometry ... µ +2 2µ ≥ 2 √ 2+1 2 > 1.9.(4.7) Annals of Mathematics Decay of geometry for unimodal maps: An elementary proof By Weixiao Shen DECAY GEOMETRY 401 Moreover...

Ngày tải lên: 16/02/2014, 05:20

... 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 structu...

Ngày tải lên: 14/02/2014, 16:20

... the discussion after the proof of Theorem 3. 2. Polar curves, affine Lefschetz theory and degree of gradient maps The use of the local polar varieties in the study of singular spaces is already ... 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 the degree of...

Ngày tải lên: 14/02/2014, 16:20

... form is even: then S is a connected sum of copies of P 1 C × P 1 C and of a K3 surface if the signature is negative, and of copies of P 1 C × P 1 C and of a K3 surface with reversed orientation if ... contradiction assuming the existence of an anti- holomorphic automorphism σ of C. Step I. G = A, where A is the group of holomorphic automorphisms of C, A := Bihol(C, C). Pro...

Ngày tải lên: 14/02/2014, 16:20

... joint continuity of Corollary 4.5. We now come to the main result of this section, the vanishing of cohomol- ogy for property Γ factors with separable predual. The heart of the proof is to show ... verify that the infinite tensor product of an arbi- trary sequence of type II 1 factors has property Γ, using the · 2 -norm density of the span of elements of the form x 1 ⊗x 2 ⊗...

Ngày tải lên: 14/02/2014, 17:20

... completes the proof of Lemma A.1. A.3. The completion of the proof Let H beaseparable Hilbert space. Denote by L(H) the Banach algebra of bounded linear operators on H, and by U(H) the subset of unitary ... 2002) Annals of Mathematics Hausdorff dimension of the set of nonergodic directions By Yitwah Cheung Annals of Mathematics, 158 (2003), 661–678 Hausdorff di...

Ngày tải lên: 14/02/2014, 17:20

... yields the claim in (2.80). This completes the proof of Lemma 6. This completes the proof of Proposition 4 and hence of Theorem 1. 3. Proof of Theorem 2 In this section we indicate how the arguments ... side of the analogue of (2.86). The integral on the right-hand side of (3.9) is of order  1/2 log(1/). Hence we get C 5/6 log(1/) for the second term on the right-hand side...

Ngày tải lên: 14/02/2014, 17:20

... 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, but also allows ... quadratic endomorphism rings. Proof. The proof of Theorem 2 shows that an element (A, B) uniquely determines the multiplication table of R, in terms of some basis 1,ω,θ. Ele...

Ngày tải lên: 14/02/2014, 17:20