eBook ISBN:  9781470401337 
Product Code:  MEMO/116/554.E 
List Price:  $38.00 
MAA Member Price:  $34.20 
AMS Member Price:  $22.80 
eBook ISBN:  9781470401337 
Product Code:  MEMO/116/554.E 
List Price:  $38.00 
MAA Member Price:  $34.20 
AMS Member Price:  $22.80 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 116; 1995; 63 ppMSC: 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 \(N \leq 2n1\).
ReadershipResearch 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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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 \(N \leq 2n1\).
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