共查询到20条相似文献,搜索用时 31 毫秒
1.
Since the early seventies flows with the Lefschetz property were studied by several authors. In this paper a Lefschetz formula
is proved for the geodesic flow of a compact locally symmetric space. The flow is described in terms of actions of split tori
of various dimensions and the geometric side of the Lefschetz formula is a sum over closed geodesics which correspond to a
given torus. The cohomological side is given in terms of Lie algebra cohomology. 相似文献
2.
Robert Laterveer 《manuscripta mathematica》2012,138(1-2):23-34
It has been remarked by Hartshorne, that Barth’s theorem for a smooth projective X follows from the strong Lefschetz theorem for the cohomology of X. Using the strong Lefschetz theorem for intersection cohomology, we give an extension of Barth’s theorem to singular X. This naturally raises several questions concerning possible Barth theorems on the level of intersection cohomology. 相似文献
3.
For a compact symplectic manifold which is s-Lefschetz which is weaker than the hard Lefschetz property, we prove that the Lefschetz decomposition for de Rham cohomology also holds. 相似文献
4.
The Hard Lefschetz theorem is known to hold for the intersection cohomology of the toric variety associated to a rational convex polytope. One can construct the intersection cohomology combinatorially from the polytope, hence it is well defined even for nonrational polytopes when there is no variety associated to it. We prove the Hard Lefschetz theorem for the intersection cohomology of a general polytope. 相似文献
5.
In this paper we prove the Lefschetz coincidence theorem in o-minimal expansions of fields using the o-minimal singular homology and cohomology. 相似文献
6.
Antoine Douai 《manuscripta mathematica》2014,145(3-4):285-317
We consider mirror symmetry (A-side vs B-side, namely singularity side) in the framework of quantum differential systems. We focuse on the logarithmic non-resonant case, which describes the geometric situation and we show that such systems provide a good framework in order to generalize the construction of the rational structure given by Katzarkov, Kontsevich and Pantev for the complex projective space. As an application, we give a closed formula for the rational structure defined by the Lefschetz thimbles on the flat sections of the Gauss-Manin connection associated with the Landau–Ginzburg models of weighted projective spaces (a class of Laurent polynomials). As a by-product, using a mirror theorem, we get a rational structure on the orbifold cohomology of weighted projective spaces. The formula on the B-side is more complicated than the one on the A-side (the latter agrees with one of Iritani’s results), depending on numerous combinatorial data which are rearranged after the mirror transformation. 相似文献
7.
Yoichi Mieda 《Mathematische Zeitschrift》2007,257(2):403-425
In this paper, we discuss a p-adic analogue of the Picard–Lefschetz formula. For a family with ordinary double points over a complete discrete valuation
ring of mixed characteristic (0,p), we construct vanishing cycle modules which measure the difference between the rigid cohomology groups of the special fiber
and the de Rham cohomology groups of the generic fiber. Furthermore, the monodromy operators on the de Rham cohomology groups
of the generic fiber are described by the canonical generators of the vanishing cycle modules in the same way as in the case
of the ℓ-adic (or classical) Picard–Lefschetz formula. For the construction and the proof, we use the logarithmic de Rham–Witt
complexes and those weight filtrations investigated by Mokrane (Duke Math. J. 72(2):301–337, 1993).
相似文献
8.
Robin Hartshorne 《manuscripta mathematica》1972,7(2):125-140
We announce the development of a theory of algebraic De Rham cohomology and homology for arbitrary schemes over a field of characteristic zero. Over the complex numbers, this theory is equivalent to singular cohomology. Applications include generalizations of theorems of Lefschetz and Barth on the cohomology of projective varieties. 相似文献
9.
In this paper we study the monodromy action on the first Betti and de Rham non-Abelian cohomology arising from a family of smooth curves. We describe sufficient conditions for the existence of a Zariski-dense monodromy orbit. In particular, we show that for a Lefschetz pencil of sufficiently high degree the monodromy action is dense. 相似文献
10.
For a Poisson algebra, we prove that the Poisson cohomology theory introduced by Flato et al.(1995)is given by a certain derived functor. We show that the(generalized) deformation quantization is equivalent to the formal deformation for Poisson algebras under certain mild conditions. Finally we construct a long exact sequence, and use it to calculate the Poisson cohomology groups via the Yoneda-extension groups of certain quasi-Poisson modules and the Lie algebra cohomology groups. 相似文献
11.
It is well known that the validity of the so called Lenard–Magri scheme of integrability of a bi-Hamiltonian PDE can be established if one has some precise information on the corresponding 1st variational Poisson cohomology for one of the two Hamiltonian operators. In the first part of the paper we explain how to introduce various cohomology complexes, including Lie superalgebra and Poisson cohomology complexes, and basic and reduced Lie conformal algebra and Poisson vertex algebra cohomology complexes, by making use of the corresponding universal Lie superalgebra or Lie conformal superalgebra. The most relevant are certain subcomplexes of the basic and reduced Poisson vertex algebra cohomology complexes, which we identify (non-canonically) with the generalized de Rham complex and the generalized variational complex. In the second part of the paper we compute the cohomology of the generalized de Rham complex, and, via a detailed study of the long exact sequence, we compute the cohomology of the generalized variational complex for any quasiconstant coefficient Hamiltonian operator with invertible leading coefficient. For the latter we use some differential linear algebra developed in the Appendix. 相似文献
12.
We prove that, for compact regular Poisson manifolds, the zeroth homology group is isomorphic to the top foliated cohomology group, and we give some applications. In particular, we show that, for regular unimodular Poisson manifolds, top Poisson and foliated cohomology groups are isomorphic. Inspired by the symplectic setting, we define what a perfect Poisson manifold is. We use these Poisson homology computations to provide families of perfect Poisson manifolds. 相似文献
13.
We deduce from Deligne's form of the Riemann hypothesis and the hard Lefschetz theoremin l-adic cohomology the corresponding facts for any “reasonable” cohomology theory, in particular for crystalline cohomology, and give some applications to algebraic cycles. 相似文献
14.
Summary For a class of self-correspondencesC calledweakly hyperbolic, we give a computable formula for the contribution of a fixed point component to the Lefschetz number ofC. The formula applies to Lefschetz numbers of cohomology with coefficients in a constructible complex of sheaves (such as intersection homology).Oblatum 9-XI-1990 & 29-IV-1992In memory of J.L. VerdierPartially supported by NSF grant # DMS8802638 and DMS9001941Partially supported by NSF grant # DMS8803083 and DMS9106522 相似文献
15.
Using the existence of certain symplectic submanifolds in symplectic 4-manifolds, we prove an estimate from above for the
number of singular fibers with separating vanishing cycles in minimal Lefschetz fibrations over surfaces of positive genus.
This estimate is then used to deduce that mapping class groups are not uniformly perfect, and that the map from their second
bounded cohomology to ordinary cohomology is not injective.
Oblatum 8-IX-2000 & 20-X-2000?Published online: 29 January 2001 相似文献
16.
Hisaaki Endo 《Mathematische Annalen》2000,316(2):237-257
We show that the cohomology class represented by Meyer's signature cocycle is of order in the 2-dimensional cohomology group of the hyperelliptic mapping class group of genus . By using the -cochain cobounding the signature cocycle, we extend the local signature for singular fibers of genus 2 fibrations due to
Y. Matsumoto [18] to that for singular fibers of hyperelliptic fibrations of arbitrary genus and calculate its values on Lefschetz singular fibers. Finally, we compare our local signature with another local signature
which arises from algebraic geometry.
Received: 6 August 1998 / in final form: 24 February 1999 相似文献
17.
Philippe Monnier 《Israel Journal of Mathematics》2002,129(1):189-207
It is known that the computation of the Poisson cohomology is closely related to the classification of singularities of Poisson
structures. In this paper, we will first look for the normal forms of germs at (0,0) of Poisson structures onG
2 (G=ℝ or ℂ) and recall a result given by Arnold. Then we will compute locally the Poisson cohomology of a particular type of
Poisson structure. 相似文献
18.
Laurent Manivel 《Inventiones Mathematicae》1997,127(2):401-416
Summary. The main result of this article is a general vanishing theorem for the cohomology of tensorial representations of an ample
vector bundle on a smooth complex projective variety. In particular, we extend classical theorems of Griffiths and Le Potier
to the whole Dolbeault cohomology, prove a variant of an uncorrect conjecture of Sommese, and answer a question of Demailly.
As an application, we prove conjectures of Debarre and Kim for branched coverings of grassmannians, and extend a well-known
Barth–Lefschetz type theorem for branched covers of projective spaces, due to Lazarsfeld. We also obtain new restriction theorems
for certain degeneracy loci.
Oblatum 10-IV-1996 & 22-V-1996 相似文献
19.
In this paper, we prove a higher Lefschetz formula for foliations in the presence of a closed Haefliger current. To this end, we associate with such a current an equivariant cyclic cohomology class of Connes' C∗-algebra of the foliation, and compute its pairing with the localized equivariant K-theory in terms of local contributions near the fixed points. 相似文献
20.
A theorem of Lambrechts and Stanley is used to find the rational cohomology of the complement of an embedding S~(4n-1)→ S~(2n)× S~m as a module and demonstrate that it is not necessarily determined by the map induced on cohomology by the embedding, nor is it a trivial extension. This demonstrates that the theorem is an improvement on the classical Lefschetz duality. 相似文献