Some Special Properties of the Adjunction Theory for 3-Folds in P5 (Memoirs of the American Mathematical Society)
( Memoirs of the American Mathematical Society )
Publication series ：Memoirs of the American Mathematical Society
Author： Mauro C. Beltrametti
Publisher： American Mathematical Society
Publication year： 2013
E-ISBN: 9781470401337
P-ISBN(Paperback): 9780821802342
Subject： O187 algebraic geometry
Keyword： Number Theory
Language： ENG
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Some Special Properties of the Adjunction Theory for 3-Folds in P5 (Memoirs of the American Mathematical Society)
Description
This work studies the adjunction theory of smooth $3$-folds in $\mathbb P^5$. Because of the many special restrictions on such $3$-folds, the structure of the adjunction theoretic reductions are especially simple, e.g. the $3$-fold equals its first reduction, the second reduction is smooth except possibly for a few explicit low degrees, and the formulae relating the projective invariants of the given $3$-fold with the invariants of its second reduction are very explicit. Tables summarizing the classification of such $3$-folds up to degree $12$ are included. Many of the general results are shown to hold for smooth projective $n$-folds embedded in $\mathbb P^N$ with $N \leq 2n-1$.