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Some Special Properties of the Adjunction Theory for \(3\)-Folds in \(\mathbb P^5\)
Mauro C. Beltrametti, Michael Schneider, and Andrew J. Sommese

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$36
Individual Members: US$21.60
Institutional Members: US$28.80
Order Code: MEMO/116/554
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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.

Table of Contents

  • Introduction
  • Background material
  • 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 \(12\)
  • References
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