Related papers: Differential forms on free and almost free divisor…

We study linear free divisors, that is, free divisors arising as discriminants in prehomogeneous vector spaces, and in particular in quiver representation spaces. We give a characterization of the prehomogeneous vector spaces containing…

We compute explicit transgression forms for the Euler and Pontrjagin classes of a Riemannian manifold $M$ of dimension 4 under a conformal change of the metric, or a change to a Riemannian connection with torsion. These formulae describe…

On a compact K\"{a}hler manifold $X$ with a holomorphic 2-form $\a$, there is an almost complex structure associated with $\a$. We show how this implies vanishing theorems for the Gromov-Witten invariants of $X$. This extends the approach,…

We introduce a natural map from the space of pure-type complex differential forms on a complex manifold to the corresponding one on the infinitesimal deformations of this complex manifold. By use of this map, we generalize an extension…

Twistor forms are a natural generalization of conformal vector fields on Riemannian manifolds. They are defined as sections in the kernel of a conformally invariant first order differential operator. We study twistor forms on compact…

This paper studies the formal deformations of differential algebra morphisms. As a consequence, we develop a cohomology theory of differential algebra morphisms to interpret the lower degree cohomology groups as formal deformations. Then,…

In this note, we show that the obstruction classes of deforming vector forms on a compact K\"ahler manifold is annihilated by cohomology classes.

We define a new version of the exterior derivative on the basic forms of a Riemannian foliation to obtain a new form of basic cohomology that satisfies Poincar\'e duality in the transversally orientable case. We use this twisted basic…

We give a complete list of formal invariants for a large class of formal differential 1-forms $\w \in \Bbb C [[ x, y]]dx + \Bbb C [[ x, y]]dy$. \indent A $\hat{SL}$-equisingular deformation is an equireducible deformation which leaves…

Concerning the problem of classifying complete submanifolds of Euclidean space with codimension two admitting genuine isometric deformations, until now the only known examples with the maximal possible rank four are the real Kaehler minimal…

We give an explicit combinatorial description of the deformation theory of the Abelian category of (quasi)coherent sheaves on any separated Noetherian scheme $X$ via the deformation theory of path algebras of quivers with relations, by…

Deformations of compact Riemann surfaces are considered using a \v{C}ech cohomology sliding overlaps approach. Cocycles are calculated for conformal cutting and regluing deformations at zeros of Abelian differentials. A second order…

We show how certain topological properties of co-K\"ahler manifolds derive from those of the K\"ahler manifolds which construct them. In particular, we show that the existence of parallel forms on a co-K\"ahler manifold reduces the…

Cheeger-Simons differential characters, Deligne cohomology in the smooth category, the Hopkins-Singer construction of ordinary differential cohomology and the recent Harvey-Lawson constructions are each in two distinct ways Abelian group…

This is the first in a series of papers about foliations in derived geometry. After introducing derived foliations on arbitrary derived stacks, we concentrate on quasi-smooth and rigid derived foliations on smooth complex algebraic…

This is partly a survey and partly a research article. Some known results and open problems about Kaehler groups (fundamental groups of compact Kaehler manifolds) are discussed. A new notion of Kaehler homomorphism is introduced. This is a…

We show that the universal abelian cover of the complement to a germ of a reducible divisor on a complex space $Y$ with isolated singularity is $(dimY-2)$-connected provided that the divisor has normal crossings outside of the singularity…

In this paper we use the results from the first part to compute the vanishing topology for matrix singularities based on certain spaces of matrices. We place the variety of singular matrices in a geometric configuration of free divisors…

In the early days of the Floer theory, Atiyah asked if there is a Milnor fiber description of the Floer homology of the links of singularities. We answer this question for the Brieskorn-Hamm complete intersection singularities. The…

As is well-known, the Witten deformation of the De Rham complex computes the De Rham cohomology. In this paper we study the Witten deformation on a noncompact manifold and restrict it to differential forms which behave polynomially near…