Related papers: Courants du type residuel attach\'es \`a une inter…
We give a construction of contact homology in the sense of Eliashberg--Givental--Hofer. Specifically, we construct coherent virtual fundamental cycles on the relevant compactified moduli spaces of pseudo-holomorphic curves.
The purpose of this paper is to point out a relation between the canonical sheaf and the intersection complex of a singular algebraic variety. We focus on the hypersurface case. Let $M$ be a complex manifold, $X\subset M$ a singular…
Regularity, complete intersection and Gorenstein properties of a local ring can be characterized by homological conditions on the canonical homomorphism into its residue field (Serre, Avramov, Auslander). It is also known that in positive…
We establish a direct classical-quantum correspondence on convex cocompact hyperbolic manifolds between the spectrums of the geodesic flow and the Laplacian acting on natural tensor bundles. This extends previous work detailing the…
We describe the behaviour at infinity of the bifurcation current in the moduli space of quadratic rational maps. To this purpose, we extend it to some closed, positive (1, 1)-current on a two-dimensional complex projective space and then…
Building on coprincipal mesoprimary decomposition [Kahle and Miller, 2014], we combinatorially construct an irreducible decomposition of any given binomial ideal. In a parallel manner, for congruences in commutative monoids we construct…
A unification of characteristic mode decomposition for all method-of-moment formulations of field integral equations describing free-space scattering is derived. The work is based on an algebraic link between impedance and transition…
Characteristic class relations in Dolbeault cohomology follow from the existence of a holomorphic geometric structure (for example, holomorphic conformal structures, holomorphic Engel distributions, holomorphic projective connections, and…
In this article we establish bounds for the Castelnuovo-Mumford regularity of projective schemes in terms of the degrees of their defining equations. The main new ingredient in our proof is to show that generic residual intersections of…
The border-collision normal form describes the local dynamics in continuous systems with switches when a fixed point intersects a switching surface. For one-dimensional cases where the bifurcation creates or destroys only fixed points and…
We study Lelong numbers of currents of full mass intersection on a compact Kaehler manifold in a mixed setting. Our main theorems cover some recent results due to Darvas-Di Nezza-Lu. One of the key ingredients in our approach is a new…
This paper is devoted to characterizing the so-called order isomorphisms intertwining the $L^2$-semigroups of two Dirichlet forms. We first show that every unitary order isomorphism intertwining semigroups is the composition of…
We deal with the complete-intersection property of maximally differential ideals. Also, we connect the Gorenstein homology of derivations to the Gorenstein property of the base rings. These equipped with some applications.
We give homotopy invariant definitions corresponding to three well known properties of complete intersections, for the ring, the module theory and the endomorphisms of the residue field, and we investigate them for the mod p cochains on a…
We give an explicit description, in terms of bracket, anchor, and pairing, of the standard cochain complex associated to a Courant algebroid. In this formulation, the differential satisfies a formula that is formally identical to the Cartan…
We track the trajectories of individual horocycles on the modular surface. Our tracking is constructive, and we thus \emph{effectively} establish topological transitivity and even line-transitivity for the horocyclic flow. We also describe…
In this paper we prove conditions for transversal intersection of monomial ideals and derive a simplicial characterization of this phenomenon.
This is an expository paper on the subject of the title. It assumes basic scheme theory, commutative and homological algebra.
Working over a field of characteristic zero, we give structure theorems for all grade three licci ideals and their minimal free resolutions. In particular, we completely classify such ideals up to deformation. The descriptions of their…
Oriented closed curves on an orientable surface with boundary are described up to continuous deformation by reduced cyclic words in the generators of the fundamental group and their inverses. By self-intersection number one means the…