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Some Special Properties of the Adjunction Theory for $$3$$-Folds in $$\mathbb P^5$$
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Memoirs of the American Mathematical Society
1995; 63 pp; softcover
Volume: 116
ISBN-10: 0-8218-0234-8
ISBN-13: 978-0-8218-0234-2
List Price: US$38 Individual Members: US$22.80
Institutional Members: US\$30.40
Order Code: MEMO/116/554

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 $$N \leq 2n-1$$.

Research mathematicians, researchers in algebraic geometry.

• The second reduction for $$n$$-folds in $$\mathbb P^{2n-1}$$
• General formulae for threefolds in $$\mathbb P^5$$
• Nefness and bigness of $$K_X+2\mathcal K$$
• Ampleness of $$K_X+2\mathcal K$$
• Nefness and bigness of $$K_X+\mathcal K$$
• Invariants for threefolds in $$\mathbb P^5$$ up to degree $$12$$