Adjunction formula (algebraic geometry)
- Adjunction formula (algebraic geometry)
In mathematics, the adjunction formula of algebraic geometry and complex manifold theory relates, for a hypersurface, its normal bundle, its canonical bundle, and the canonical bundle of the ambient variety or manifold.
Let "H" be a hypersurface in a complex manifold "M". The "adjunction formula" reads
:,
where is the canonical bundle of "M", and the notation denotes its restriction to "H". Additionally, is the normal bundle of "H" in "M", and is the line bundle associated to "H" as a Cartier divisor, restricted to "H" (sometimes written ). For a proof, see [GH94] , page 146-147.
References
*cite book
author = Phillip Griffiths
coauthors = Joe Harris
year = 1994
title = Principles of Algebraic Geometry
publisher = Wiley-Interscience
id = ISBN 0-471-05059-8
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