ISSN:
1570-5846
Keywords:
adjunction formula
;
regular differential forms
;
relative duality
;
fundamental class.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Let $$f:X \to Y$$ be a morphism of noetherian schemes,generically smooth and equidimensional of dimension $$d,\iota :X\prime \to X$$ a closed embedding such that $$f \circ \iota :X\prime \to Y$$ is generically smooth and equidimensional ofdimension d $$\prime $$ , and X $$\prime $$ , X and Y are excellent schemes withoutembedded components. We exhibit a concrete morphism $$Res_{X\prime /X} :det \mathcal{N}_{X\prime /X} \otimes _{\mathcal{O}_{X\prime } } \iota *\omega _{X/Y}^d \to \omega _{X\prime /Y\prime }^{d\prime } ,$$ which transforms the integral of X/Y into the integral ofX $$\prime $$ /Y. Here $$\mathcal{N}_{X\prime /X} $$ denotes the normal sheaf of X $$\prime $$ /X and $$\omega _{X/Y}^d $$ resp. $$\omega _{X\prime /Y\prime }^{d\prime } $$ denotes the sheaf ofregular differential forms of X/Y resp. X $$\prime $$ /Y. Usinggeneralized fractions we provide a canonical description ofresidual complexes and residue pairs of Cohen--Macaulayvarieties, and obtain a very explicit description of fundamentalclasses and their traces.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1000141319604
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