Intersection Multiplicities in Commutative Algebra
Intersection Numbers of Sections of Elliptic Surfaces.
Intersection of analytic curves
We give a relation between two theories of improper intersections, of Tworzewski and of Stückrad-Vogel, for the case of algebraic curves. Given two arbitrary quasiprojective curves V₁,V₂, the intersection cycle V₁ ∙ V₂ in the sense of Tworzewski turns out to be the rational part of the Vogel cycle v(V₁,V₂). We also give short proofs of two known effective formulae for the intersection cycle V₁ ∙ V₂ in terms of local parametrizations of the curves.
Intersection rings of spaces of triangles
Intersection theory and separation exponent in complex analytic geometry
We consider the intersection multiplicity of analytic sets in the general situation. We prove that it is a regular separation exponent for complex analytic sets and so it estimates the Łojasiewicz exponent. We also give some geometric properties of proper projections of analytic sets.
Intersection theory in complex analytic geometry
We present a construction of an intersection product of arbitrary complex analytic cycles based on a pointwise defined intersection multiplicity.
Intersection Theory of Projective Linear Spaces.
Intersection theory on algebraic stacks and on their moduli spaces.
Intersection theory on Deligne-Mumford compactifications
Intersection theory using Adams operations.
Intersections of higher weight cycles and modular forms
Intersections of Projective Varieties and Generic Projections.
Intersection-theoretical computations on
In this paper we explore several concrete problems, all more or less related to the intersection theory of the moduli space of (stable) curves, introduced by Mumford [Mu 1].
Invariance of tautological equations I: conjectures and applications
The main goal of this paper is to introduce a set of conjectures on the relations in the tautological rings. In particular, this framework gives an efficient algorithm to calculate all tautological equations using only finite-dimensional linear algebra. Other applications include the proofs of Witten’s conjecture on the relations between higher spin curves and Gelfand–Dickey hierarchy and Virasoro conjecture for target manifolds with conformal semisimple quantum cohomology, both for genus up to...
Isolated intersection multiplicity and regular separation of analytic sets
An isolated point of intersection of two analytic sets is considered. We give a sharp estimate of their regular separation exponent in terms of intersection multiplicity and local degrees.
Joins and intersections.
Joins, tangencies and intersections.
K3 surfaces: moduli spaces and Hilbert schemes.
L1-cohomology of normal algebraic surfaces. I.
L2 and intersection cohomologies for a polarizable Variation of Hodge structure.