Tài liệu Đề tài " Moduli space of principal sheaves over projective varieties " pptx

... pullbacks, (E 1 ,ϕ 1 ) and (E 2 ,ϕ 2 ), of (E R 1 ,ϕ R 1 ), Annals of Mathematics, 161 (2005), 1037–1092 Moduli space of principal sheaves over projective varieties By Tom ´ as G ´ omez and Ignacio ... fixing the Chern classes of E and of the line bundles associated to the principal bundle P and characters of G, we obtain a projective moduli space of semista...

Ngày tải lên: 16/02/2014, 05:20

... identification of ΩE d 2 with the space of elliptic differentials of degree d. Abelian varieties. Let A g denote the moduli space of principally polarized Abelian varieties of dimension g. The space A g is ... 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 co...

Ngày tải lên: 16/02/2014, 06:20

... 483–515. [Cat2] , Automorphisms of rational double points and moduli spaces of surfaces of general type, Compositio Math. 61 (1987), 81–102. [Cat3] , Connected components of moduli spaces, J. Differential ... 13, 2001) Annals of Mathematics Moduli spaces of surfaces and real structures By Fabrizio Catanese* Annals of Mathematics, 158 (2003), 577–592 Moduli...

Ngày tải lên: 14/02/2014, 16:20

... 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 ... +1 .(II.1.18) Since Area(T s ) is a monotonic function of s, a standard argument then gives (II.1.16). Annals of Mathematics The space of embedded minimal surfaces o...

Ngày tải lên: 14/02/2014, 17:20

... 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

... 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 a classical ... invariant of the hy- persurface F t and is denoted by P(F t ). Note that P (F t ) corresponds exactly to the classical notion of class of a projective hypersurface; see [L]....

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

... in the proof of Theorem 5. Lemma A.1. Let L be a G δ -subset of a σ-compact metric space K.Let P be a Polish space (aspace with a complete metric topology). Let H be an F σ -subset of the cartesian ... 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...

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

... of points in the space of 2 × 3 × 3 integer boxes correspond to the unit groups of orders in cubic fields. We similarly determine the stabilizers over Z of the other two spaces of forms indicated ... 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