Titlebook: Intersection Theory; William Fulton Book 1984 Springer-Verlag Berlin Heidelberg 1984 Algebraische Geometrie.Blowing up.Divisor.Schnittheor

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Riemann-Roch for Non-singular Varieties,The Grothendieck-Riemann-Roch theorem (GRR) states that for a proper morphism .: . → . of non-singular varieties,.for all α in the Grothendieck group of vector bundles, or of coherent sheaves, on .. When . is a point, one recovers Hirzebruch’s formula (HRR) for the Euler characteristic of a vector bundle . on .:..

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浮夸

Intersection Multiplicities,f dimension . − ., the intersection multiplicity . (., . · .; .) is defined to be the coefficient of . in the intersection class . · . ∈ ..(.). The intersection multiplicity is a positive integer, satisfying..

Capitulate

Positivity,rsection class has a corresponding decomposition into Σ .. α., α. ∈ ..(..), (..)=Supp(..). If the bundle . is suitably positive, one can deduce corresponding positivity of the intersection classes, even if the intersections are not proper.

断言

Bivariant Intersection Theory,or all .′ → ., .′ = . ×..′, all .. In this chapter we formalize the study of such operations. For any morphism .: . → ., a . in . is a collection of homomorphisms from ...′ to ...′, for all .′ → ., all ., compatible with push-forward, pull-back, and intersection products.

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Riemann-Roch for Singular Varieties,ff a closed subset .. This produces a localized Chern character.. which lives in the bivariant group . (.→.).. For each class α ∈ ..., this gives a class.whose image in .... is ∑(−1). ch (..) ∩ α. The properties needed for Riemann-Roch, in particular the invariance under rational deformation, follow from the bivariant nature of ..

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