# Category: Intersection theory

Residual intersection
In algebraic geometry, the problem of residual intersection asks the following: Given a subset Z in the intersection of varieties, understand the complement of Z in the intersection; i.e., the residua
Normal cone
In algebraic geometry, the normal cone of a subscheme of a scheme is a scheme analogous to the normal bundle or tubular neighborhood in differential geometry.
Segre class
In mathematics, the Segre class is a characteristic class used in the study of cones, a generalization of vector bundles. For vector bundles the total Segre class is inverse to the total Chern class,
Bézout's theorem
Bézout's theorem is a statement in algebraic geometry concerning the number of common zeros of n polynomials in n indeterminates. In its original form the theorem states that in general the number of
Intersection homology
In topology, a branch of mathematics, intersection homology is an analogue of singular homology especially well-suited for the study of singular spaces, discovered by Mark Goresky and Robert MacPherso
Intersection theory
In mathematics, intersection theory is one of the main branches of algebraic geometry, where it gives information about the intersection of two subvarieties of a given variety. The theory for varietie
Chow group
In algebraic geometry, the Chow groups (named after Wei-Liang Chow by Claude Chevalley) of an algebraic variety over any field are algebro-geometric analogs of the homology of a topological space. The
Enumerative geometry
In mathematics, enumerative geometry is the branch of algebraic geometry concerned with counting numbers of solutions to geometric questions, mainly by means of intersection theory.
Virtual fundamental class
In mathematics, specifically enumerative geometry, the virtual fundamental class of a space is a replacement of the classical fundamental class in its chow ring which has better behavior with respect
Hodge index theorem
In mathematics, the Hodge index theorem for an algebraic surface V determines the signature of the intersection pairing on the algebraic curves C on V. It says, roughly speaking, that the space spanne
Serre's multiplicity conjectures
In mathematics, Serre's multiplicity conjectures, named after Jean-Pierre Serre, are certain purely algebraic problems, in commutative algebra, motivated by the needs of algebraic geometry. Since Andr
Steiner's conic problem
In enumerative geometry, Steiner's conic problem is the problem of finding the number of smooth conics tangent to five given conics in the plane in general position. If the problem is considered in th
Fulton–Hansen connectedness theorem
In mathematics, the Fulton–Hansen connectedness theorem is a result from intersection theory in algebraic geometry, for the case of subvarieties of projective space with codimension large enough to ma