共查询到20条相似文献,搜索用时 46 毫秒
1.
Julien Grivaux 《Mathematische Annalen》2010,347(2):249-284
In this article, we construct Chern classes in rational Deligne cohomology for coherent sheaves on a smooth complex compact
manifold. We prove that these classes satisfy the functoriality property under pullbacks, the Whitney formula and the Grothendieck–Riemann–Roch
theorem for projective morphisms between smooth complex compact manifolds. 相似文献
2.
In this paper, we consider the weight i de Rham–Gauss–Manin bundles on a smooth variety arising from a smooth projective morphism for . We associate to each weight i de Rham bundle, a certain parabolic bundle on S and consider their parabolic Chern characters in the rational Chow groups, for a good compactification S of U. We show the triviality of the alternating sum of these parabolic bundles in the (positive degree) rational Chow groups.
This removes the hypothesis of semistable reduction in the original result of this kind due to Esnault and Viehweg. 相似文献
3.
We establish a—and conjecture further—relationship between the existence of subvarieties representing minimal cohomology classes
on principally polarized abelian varieties, and the generic vanishing of the cohomology of twisted ideal sheaves. The main
ingredient is the Generic Vanishing criterion established in Pareschi G. and Popa M. (GV-sheaves, Fourier–Mukai transform, and Generic Vanishing. Preprint math.AG/0608127), based on the Fourier–Mukai transform.
MP was partially supported by the NSF grant DMS 0500985 and by an AMS Centennial Fellowship. 相似文献
4.
We show that for each discrete group Γ, the rational assembly map
is injective on classes dual to , where Λ* is the subring generated by cohomology classes of degree at most 2 (and where the pairing uses the Chern character). Our
result implies homotopy invariance of higher signatures associated to classes in Λ*. This consequence was first established by Connes–Gromov–Moscovici (Geom. Funct. Anal. 3(1): 1–78, 1993) and Mathai (Geom.
Dedicata 99: 1–15, 2003). Note, however that the above injectivity statement does not follow from their methods. Our approach
is based on the construction of flat twisting bundles out of sequences of almost flat bundles as first described in our work
(Hanke and Schick, J. Differential Geom. 74: 293–320, 2006). In contrast to the argument in Connes-Gromov-Moscovici (Geom.
Funct.Anal. 3(1): 1–78, 1993), our approach is independent of (and indeed gives a new proof of) the result of Hilsum–Skandalis
(J. Reine Angew. Math. 423: 73–99, 1999) on the homotopy invariance of the index of the signature operator twisted with bundles
of small curvature.
相似文献
5.
We study Miyaoka-type semistability criteria for principal Higgs G-bundles E on complex projective manifolds of any dimension. We prove that E has the property of being semistable after pullback to any projective curve if and only if certain line bundles, obtained from some characters of the parabolic subgroups of G, are numerically effective. One also proves that these conditions are met for semistable principal Higgs bundles whose adjoint bundle has vanishing second Chern class.In a second part of the paper, we introduce notions of numerical effectiveness and numerical flatness for principal (Higgs) bundles, discussing their main properties. For (non-Higgs) principal bundles, we show that a numerically flat principal bundle admits a reduction to a Levi factor which has a flat Hermitian–Yang–Mills connection, and, as a consequence, that the cohomology ring of a numerically flat principal bundle with coefficients in R is trivial. To our knowledge this notion of numerical effectiveness is new even in the case of (non-Higgs) principal bundles. 相似文献
6.
Ettore Aldrovandi 《Journal of Pure and Applied Algebra》2008,212(5):994-1038
We define 2-gerbes bound by complexes of braided group-like stacks. We prove a classification result in terms of hypercohomology groups with values in abelian crossed squares and cones of morphisms of complexes of length 3. We give an application to the geometric construction of certain elements in Hermitian Deligne cohomology groups. 相似文献
7.
Hélène Esnault 《K-Theory》1992,6(1):45-56
On a smooth varietyX defined over a fieldK of characteristic zero, one defines characteristic classes of bundles with an integrableK-connection in a group lifting the Chow group, which map, whenK is the field of complex numbers andX is proper, to Cheeger-Simons' secondary analytic invariants, compatibly with the cycle map in the Deligne cohomology. 相似文献
8.
Adrian Langer 《Mathematische Zeitschrift》2000,235(3):591-614
We define Chern classes of reflexive sheaves using Wahl's relative local Chern classes of vector bundles. The main result
of the paper bounds contributions of singularities of a sheaf to the Riemann–Roch formula. Using it we are able to prove inequality
in Wahl's conjecture on relative asymptotic RR formula for rank 2 vector bundles. Moreover, we prove that if Wahl's conjecture
is true for a singularity then it is true for any its quotient. This implies Wahl's conjecture for quotient singularities
and for quotients of cones over elliptic curves.
Received March 2, 1998; in final form March 24, 1999 / Published online September 14, 2000 相似文献
9.
Yasunari Nagai 《Mathematische Zeitschrift》2008,258(2):407-426
We study the monodromy operators on the Betti cohomologies associated to a good degeneration of irreducible symplectic manifold
and we show that the unipotency of the monodromy operator on the middle cohomology is at least the half of the dimension.
This implies that the “mildest” singular fiber of a good degeneration with non-trivial monodromy of irreducible symplectic
manifolds is quite different from the generic degeneration of abelian varieties or Calabi–Yau manifolds. 相似文献
10.
We study the restriction to smaller subgroups, of cohomology classes on arithmetic groups (possibly after moving the class
by Hecke correspondences), especially in the context of first cohomology of arithmetic groups. We obtain vanishing results for the first cohomology of cocompact arithmetic lattices in SU(n,1) which arise from hermitian forms over division algebras D of degree p
2, p an odd prime, equipped with an involution of the second kind. We show that it is not possible for a ‘naive’ restriction of
cohomology to be injective in general. We also establish that the restriction map is injective at the level of first cohomology
for non co-compact lattices, extending a result of Raghunathan and Venkataramana for co-compact lattices.
Received: 14 September 2000 / Accepted: 6 June 2001 相似文献
11.
Atiyah and Bott used equivariant Morse theory applied to theYang–Mills functional to calculate the Betti numbers ofmoduli spaces of vector bundles over a Riemann surface, rederivinginductive formulae obtained from an arithmetic approach whichinvolved the Tamagawa number of SLn. This article attempts tosurvey and extend our understanding of this link between Yang–Millstheory and Tamagawa numbers, and to explain how methods usedover the last three decades to study the singular cohomologyof moduli spaces of bundles on a smooth projective curve over can be adapted to the setting of 1-homotopy theory to studythe motivic cohomology of these moduli spaces over an algebraicallyclosed field. 相似文献
12.
Marius Crainic 《Commentarii Mathematici Helvetici》2003,78(4):681-721
In the first section we discuss Morita invariance of
differentiable/algebroid cohomology.In the second section we extend the Van Est isomorphism to
groupoids. As a first application we clarify the connection
between differentiable and algebroid cohomology (proved in
degree 1, and conjectured in degree 2 by Weinstein-Xu
[50]). As a second application we extend Van Ests
argument for the integrability of Lie algebras. Applied to
Poisson manifolds, this immediately implies the integrability
criterion of Hector-Dazord [14].In the third section we describe the relevant characteristic classes of
representations, living in algebroid cohomology, as well as
their relation to the Van Est map. This extends
Evens-Lu-Weinsteins characteristic class $\theta_{L}$
[20] (hence, in particular, the modular class of Poisson
manifolds), and also the classical characteristic classes of
flat vector bundles [2, 30].In the last section we
describe applications to Poisson geometry. 相似文献
13.
Deligne cohomology can be viewed as a differential refinement of integral cohomology, hence captures both topological and geometric information. On the other hand, it can be viewed as the simplest nontrivial version of a differential cohomology theory. While more involved differential cohomology theories have been explicitly twisted, the same has not been done to Deligne cohomology, although existence is known at a general abstract level. We work out what it means to twist Deligne cohomology, by taking degree one twists of both integral cohomology and de Rham cohomology. We present the main properties of the new theory and illustrate its use with examples and applications. Given how versatile Deligne cohomology has proven to be, we believe that this explicit and utilizable treatment of its twisted version will be useful. 相似文献
14.
Christian Liedtke 《Mathematische Annalen》2009,343(3):623-637
A non-classical Godeaux surface is a minimal surface of general type with χ = K
2 = 1 but with h
01 ≠ 0. We prove that such surfaces fulfill h
01 = 1 and they can exist only over fields of positive characteristic at most 5. Like non-classical Enriques surfaces they fall
into two classes: the singular and the supersingular ones. We give a complete classification in characteristic 5 and compute
their Hodge-, Hodge–Witt- and crystalline cohomology (including torsion). Finally, we give an example of a supersingular Godeaux
surface in characteristic 5. 相似文献
15.
We give explicit examples of degree 3 cohomology classes not Poincaré dual to submanifolds, and discuss the realisability
of homology classes by submanifolds with Spinc normal bundles.
Received: 20 November 2001 相似文献
16.
Indranil Biswas 《Journal of Pure and Applied Algebra》2008,212(10):2298-2306
We study certain moduli spaces of stable vector bundles of rank 2 on cubic and quartic threefolds. In many cases under consideration, it turns out that the moduli space is complete and irreducible and a general member has vanishing intermediate cohomology. In one case, all except one component of the moduli space has such vector bundles. 相似文献
17.
Izzet Coskun 《Advances in Mathematics》2011,(4):2441
This paper develops a new method for studying the cohomology of orthogonal flag varieties. Restriction varieties are subvarieties of orthogonal flag varieties defined by rank conditions with respect to (not necessarily isotropic) flags. They interpolate between Schubert varieties in orthogonal flag varieties and the restrictions of general Schubert varieties in ordinary flag varieties. We give a positive, geometric rule for calculating their cohomology classes, obtaining a branching rule for Schubert calculus for the inclusion of the orthogonal flag varieties in Type A flag varieties. Our rule, in addition to being an essential step in finding a Littlewood–Richardson rule, has applications to computing the moment polytopes of the inclusion of SO(n) in SU(n), the asymptotic of the restrictions of representations of SL(n) to SO(n) and the classes of the moduli spaces of rank two vector bundles with fixed odd determinant on hyperelliptic curves. Furthermore, for odd orthogonal flag varieties, we obtain an algorithm for expressing a Schubert cycle in terms of restrictions of Schubert cycles of Type A flag varieties, thereby giving a geometric (though not positive) algorithm for multiplying any two Schubert cycles. 相似文献
18.
Julianna S. Tymoczko 《Selecta Mathematica, New Series》2007,13(2):353-367
Regular nilpotent Hessenberg varieties form a family of subvarieties of the flag variety arising in the study of quantum cohomology,
geometric representation theory, and numerical analysis. In this paper we construct a paving by affines of regular nilpotent
Hessenberg varieties for all classical types, generalizing results of De Concini–Lusztig–Procesi and Kostant. This paving
is in fact the intersection of a particular Bruhat decomposition with the Hessenberg variety. The nonempty cells of the paving
and their dimensions are identified by combinatorial conditions on roots. We use the paving to prove these Hessenberg varieties
have no odd-dimensional homology.
相似文献
19.
20.
We construct torus bundles over locally symmetric varieties associated to cocycles in the cohomology group , where Γ is a discrete subgroup of a semisimple Lie group and L is a lattice in a real vector space. We prove that such a torus bundle has a canonical complex structure and that the space
of holomorphic forms of the highest degree on a fiber product of such bundles is isomorphic to the space of mixed automorphic
forms of a certain type.
(Received 4 September 1998) 相似文献