Titlebook: Intersection Theory; William Fulton Book 1998Latest edition Springer-Verlag Berlin Heidelberg 1998 Chern class.Division.Divisor.Equivalenc

Cumbersome

Vector Bundles and Chern Classes,singular vector bundles” — there is a natural analogue of Segre classes, but not Chern classes. Segre classes for normal cones have other remarkable properties not shared by Chern classes (cf. § 4.2).

CON

Cones and Segre Classes,back..Segre classes arise naturally in many areas of algebraic geometry. Some of these occurrences are discussed in the examples and in the last two sections, which are not required for later chapters.

Outwit

Intersection Products,gular of codimension ., then ....... is the quotient bundle, there is an excess intersection formula.Given . as above, and a morphism ., form the fibre square.There are refined Gysin homomorphisms. determined by the formula i.[.] = .·. for subvarieties .of Y’..In this chapter the fundamental propert

模仿

Intersections on Non-singular Varieties,ersection products and multiplicities follow readily from the general properties proved in Chaps. 6 and 7..Bézout’s theorem, in its simplest form, states that.where . is the class of a hyperplane. A deeper analysis of intersections on projective space will be given in Chap. 12.

indemnify

滑动

Families of Algebraic Cycles,an algebraic family of zero-cycles, on a scheme which is proper over the parameter space, all the cycles have the same degree. Second, as mentioned above, the operations of intersection theory preserve algebraic families..Refined intersection theory yields an improvement over classical formulations

尖

Dynamic Intersections,l data..This allows a dynamic interpretation for the distinguished varieties and their equivalences, which can be useful for calculations. For any closed subset . of ., let (.). be the part of . supported on . (§ 6.1). If ... is generated by its sections, there is an open set . (Z) of sections such

Torrid

Positivity, theorem follows:.,.where the Z. are the distinguished varieties; all irreducible components of ∩. V. are included among the Z...There are also applications to intersection multiplicities. For example, if…, V. meet properly at a non-singular point . of an n-dimensional variety ., and.are the blow-up

Proclaim

Rationality,e, i.e. . is proper over the ground field ., and α ..... is a 0-cycle on ., the degree of a is the sum.where . is the residue field of at ., and . is the degree of the field extension. Rationally equivalent 0-cycles have the same degree (§ 1.4)..For example, if is the field of real numbers (or an ar

Coterminous