Related papers: Affine hyperplane arrangements at finite distance
We compute the graded rank of the cohomology of the hyperplane complement associated with a quaternionic reflection group, and observe that it factors into irreducible factors with positive integer coefficients. For an irreducible group,…
Following Weinstein, Boyarchenko-Weinstein and Imai-Tsushima, we construct a family of affinoids in the Lubin-Tate perfectoid space and formal models such that the cohomology of the reduction of each formal model realizes the local…
Let A be a (central) arrangement of hyperplanes in a finite dimension complex vector space V. Let M(A) be the dependence matroid determined by A. The Orlik-Solomon algebra OS(M) of a matroid M is the exterior algebra on the points modulo…
We consider orbit configuration spaces associated to finite groups acting freely by orientation preserving homeomorphisms on the $2$-sphere minus a finite number of points. Such action is equivalent to a homography action of a finite…
Graded skew-commutative rings occur often in practice. Here are two examples: 1) The cohomology ring of a compact three-dimensional manifold. 2) The cohomology ring of the complement of a hyperplane arrangement (the Orlik-Solomon algebra).…
Given a free group $F_n$, a fully irreducible automorphism $f \in \aut$, and a generic element $x \in F_n$, the elements $f^k(x)$ converge in the appropriate sense to an object called an attracting lamination of $f$. When the action of $f$…
We compute the p-adic geometric pro-\'etale cohomology of the affine space (in any dimension). This cohomogy is non-zero, contrary to the \'etale cohomology, and can be described by means of differential forms.
Let $Y=\Gamma\backslash H^n$ be a quotient of the hyperbolic space by the action of a discrete convex-cocompact group of isometries. We describe certain spaces of $\Gamma$-invariant currents on the sphere at infinity of $H^n$ with support…
We construct Morse homology groups associated with any regular function on a smooth complex algebraic variety, allowing singular and non-compact critical loci. These groups are generated by critical points of a certain large pertubation of…
We establish a general theory for projective dimensions of the logarithmic derivation modules of hyperplane arrangements. That includes the addition-deletion and restriction theorem, Yoshinaga-type result, and the division theorem for…
This dissertation describes the space of heteroclinic orbits for a class of semilinear parabolic equations, focusing primarily on the case where the nonlinearity is a second degree polynomial with variable coefficients. Along the way, a new…
To a pair (X,f), X compact ANR and f a continuous angle valued map defined on X, a fixed field and a nonnegative integer one assigns a finite configuration of complex numbers with multiplicities located in the punctured complex plane and a…
It is proved that the associative differential graded algebra of (polynomial) polyvector fields on a vector space (may be infinite- dimensional) is quasi-isomorphic to the corresponding cohomological Hochschild complex of (polynomial)…
In these notes we study hyperplane arrangements having at least one logarithmic derivation of degree two that is not a combination of degree one logarithmic derivations. It is well-known that if a hyperplane arrangement has a linear…
We study homological invariants of \'etale groupoids arising from Smale spaces, continuing on our previous work, but going beyond the stably disconnected case by incorporating resolutions in the space direction. We show that the homology…
Based on projective representations of smooth Deligne cohomology groups, we introduce an analogue of the space of conformal blocks to compact oriented (4k+2)-dimensional Riemannian manifolds with boundary. For the standard…
Let $\mathcal{C}$ be a smooth, projective and geometrically integral curve defined over a finite field $\mathbb{F}$. Let $A$ be the ring of function of $\mathcal{C}$ that are regular outside a closed point $P$ and let $k=\mathrm{Quot}(A)$.…
We show that closures of families of unitary local systems on quasiprojective varieties for which the dimension of a graded component of Hodge filtration has a constant value can be identified with a finite union of polytopes. We also…
Graded skew-commutative rings occur often in practice. Here are two examples: 1) The cohomology ring of a compact three-dimensional manifold. 2) The cohomology ring of the complement of a hyperplane arrangement (the Orlik-Solomon algebra).…
In this paper we explore a relationship between the topology of the complex hyperplane complements $\mathcal{M}_{BC_n} (\mathbb{C})$ in type B/C and the combinatorics of certain spaces of degree-$n$ polynomials over a finite field…