Related papers: Intersection homology D-Modules and Bernstein poly…

Let $k$ be a field of characteristic zero and I an ideal defining an arrangement of linear subspaces in the affine space $A^n_k$. We compute the D-module theoretic characteristic cycle of the local cohomology modules $H^r_I(k[x_1,...,x_n])$…

Black hole generalized p-brane solutions for a wide class of intersection rules are presented. The solutions are defined on a manifold that contains a product of n - 1 Ricci-flat internal spaces. They are defined up to moduli functions H_s…

We consider the problem of complex interpolation of certain Hardy-type subspaces of K\"othe function spaces. For example, suppose $X_0$ and $X_1$ are K\"othe function spaces on the unit circle $\bold T,$ and let $H_{X_0}$ and $H_{X_1}$ be…

The $L^2$-cohomology of a locally symmetric variety is known to have the topological interpretation as the intersection homology of its Baily-Borel Satake compactification. In this article, we observe that even without the Hermitian…

We consider generalized complete intersection manifolds in the product space of projective spaces, and work out useful aspects pertaining to the cohomology of sheaves over them. First, we present and prove a vanishing theorem on the…

Motivated by analogies with basic density theorems in analytic number theory, we introduce a notion (and variations) of the homological density of one space in another. We use Weil's number field/ function field analogy to predict…

Consider a real algebraic variety, $\R X$, of dimension $d$. If its complexification, $\C X$, is a rational homology manifold (at least in a neighborhood of $\R X$), then the intersection form in $\C X$ defines a bilinear form in…

This paper extends some results of Hatcher and Quinn beyond the metastable range. We give a bordism theoretic obstruction to deforming a map between manifolds simultaneously off of a collection of pairwise disjoint submanifolds under the…

Let $X$ be a compact K\"ahler manifold and $\alpha$ be a class in the Dolbeault cohomology class of bidegree $(1, 1)$ on $X$. When the numerical dimension of $\alpha$ is one and $\alpha$ admits at least two smooth semi-positive…

We compute the Poisson cohomology of a class of Poisson manifolds that are symplectic away from a collection $D$ of hypersurfaces. These Poisson structures induce a generalization of symplectic and cosymplectic structures, which we call a…

We construct a rational homotopy-theoretic model for a classifying space of locally conformally symplectic structures on four-manifolds, and use it to definition a cobordism category of three-manifolds `anchored' by principal $\Omega^2 S^2$…

We introduce neural networks to compute numerical Ricci-flat CY metrics for complete intersection and Kreuzer-Skarke Calabi-Yau manifolds at any point in K\"ahler and complex structure moduli space, and introduce the package cymetric which…

We study the intersection form $F_X$ on the second cohomology group $H^2(X, \mathbb{Z})$ of a compact K\"ahler manifold $X$ of dimension $n$. Although the structure of $F_X$ is relatively well understood in dimensions two and three, much…

For a normal variety X defined over an algebraically closed field with an action of the multiplicative group G_m, we consider the ``hyperbolic localization'' functor from D^b(X) to D^b(X^T), which localizes using closed supports in the…

We study the homology groups of the complement of a complexified real line arrangement with coefficients in complex rank-one local systems. Using Borel--Moore homology, we establish an algorithm computing their dimensions via the real…

Using a cap product, we construct an explicit Poincar\'e duality isomorphism between the blown-up intersection cohomology and the Borel-Moore intersection homology, for any commutative ring of coefficients and second-countable, oriented…

Almost hypercomplex manifolds with Hermitian and anti-Hermitian metrics are considered. A linear connection $D$ is introduced such that the structure of these manifolds is parallel with respect to D. Of special interest is the class of the…

We review some cohomological aspects of complex and hypercomplex manifolds and underline the differences between both realms. Furthermore, we try to highlight the similarities between compact complex surfaces on one hand and compact…

In these notes, we describe several geometric interpretations of $H^2(X)$ when $X$ is a trisected 4-manifold. The main insight is that, by analogy with Hodge theory and sheaf cohomology in algebraic geometry, classes in $H^2(X)$ can be…

We view Dolbeault-Morse-Novikov cohomology H^{p,q}_\eta(X) as the cohomology of the sheaf \Omega_{X,\eta}^p of \eta-holomorphic p-forms and give several bimeromorphic invariants. Analogue to Dolbeault cohomology, we establish the…