Cumbersome
发表于 2025-3-30 11:41:44
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
发表于 2025-3-30 12:47:01
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
发表于 2025-3-30 18:05:15
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
发表于 2025-3-31 00:14:49
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
发表于 2025-3-31 02:59:46
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滑动
发表于 2025-3-31 08:19:03
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
发表于 2025-3-31 10:57:13
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
发表于 2025-3-31 14:32:35
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
发表于 2025-3-31 20:01:03
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
发表于 2025-4-1 01:23:05
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