We give a quantum version of the Danilov-Jurkiewicz presentation of the cohomology of a compact toric orbifold with projective coarse moduli space. More precisely, we construct a canonical isomorphism from a formal version of the Batyrev ring from [5] to the quantum orbifold cohomology in a formal neighborhood of a canonical bulk deformation. This isomorphism generalizes results of Givental [21...

In this study, we compute simplicial cohomology groups with different coefficients of a connected sum of certain minimal simple surfaces by using the universal coefficient theorem for cohomology groups. The method used in this paper is a different way to compute digital cohomology groups of minimal simple surfaces. We also prove some theorems related to degree properties of a map on digital sph...

Generalizing the work of Lubin in the one dimensional case, conditions are found for the existence of canonical subgroups of finite height commutative formal groups of arbitrary dimension over local rings of mixed characteristic (0, p). These are p-torsion subgroups which are optimally close to being kernels of Frobenius homomorphisms. The Fp ranks of the first flat cohomology groups of these c...

Using local cohomology and algebraic D-Modules, we generalize a comparison theorem between relative de Rham cohomology and Dwork cohomology due to N. Katz, A. Adolphson and S. Sperber.

Given a compact Kähler manifold, we consider the complement U of a divisor with normal crossings and a unitary local system g̃ on it. We consider a differential graded Lie algebra of forms with holomorphic logarithmic singularities and vanishing residues. We construct a spectral sequence converging to the L2 cohomology H •(U, g̃)(2) corresponding to the anti-holomorphic filtration of this algebra...

In this note we describe aspects of the cohomology of coherent sheaves on a complete toric variety X over a field k and, more generally, the local cohomology, with supports in a monomial ideal, of a finitely generated module over a polynomial ring S. This leads to an efficient way of computing such cohomology, for which we give explicit algorithms. The problem is finiteness. The ith local cohom...

For a closed Kähler manifold with a Hamiltonian action of a connected compact Lie group by holomorphic isometries, we construct a formal Frobenius manifold structure on the equivariant cohomology by exploiting a natural DGBV algebra structure on the Cartan model. The notion of Frobenius manifolds was introduced by Dubrovin [11, 12]. It gives a coordinate free formulation of solutions to the WDV...