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Some Special Properties of the Adjunction Theory for $3$-Folds in $\mathbb P^5$
 
Mauro C. Beltrametti University Degli Studi di Genova, Genova, Italy
Andrew J. Sommese University of Notre Dame, Notre Dame, IN
Front Cover for Some Special Properties of the Adjunction Theory for 3-Folds in P^5
Available Formats:
Electronic ISBN: 978-1-4704-0133-7
Product Code: MEMO/116/554.E
List Price: $38.00
MAA Member Price: $34.20
AMS Member Price: $22.80
Front Cover for Some Special Properties of the Adjunction Theory for 3-Folds in P^5
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  • Front Cover for Some Special Properties of the Adjunction Theory for 3-Folds in P^5
  • Back Cover for Some Special Properties of the Adjunction Theory for 3-Folds in P^5
Some Special Properties of the Adjunction Theory for $3$-Folds in $\mathbb P^5$
Mauro C. Beltrametti University Degli Studi di Genova, Genova, Italy
Andrew J. Sommese University of Notre Dame, Notre Dame, IN
Available Formats:
Electronic ISBN:  978-1-4704-0133-7
Product Code:  MEMO/116/554.E
List Price: $38.00
MAA Member Price: $34.20
AMS Member Price: $22.80
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1161995; 63 pp
    MSC: Primary 14;

    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 \(N \leq 2n-1\).

    Readership

    Research mathematicians, researchers in algebraic geometry.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • 0. Background material
    • 1. The second reduction for $n$-folds in $\mathbb {P}^{2n - 1}$
    • 2. General formulae for threefolds in $\mathbb {P}^5$
    • 3. Nefness and bigness of $K_X + 2\mathcal {K}$
    • 4. Ampleness of $K_X + 2\mathcal {K}$
    • 5. Nefness and bigness of $K_X + \mathcal {K}$
    • 6. Invariants for threefolds in $\mathbb {P}^5$ up to degree 12
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Volume: 1161995; 63 pp
MSC: Primary 14;

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 \(N \leq 2n-1\).

Readership

Research mathematicians, researchers in algebraic geometry.

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