| eBook 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 |
| eBook 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 |
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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 \(N \leq 2n-1\).
ReadershipResearch mathematicians, researchers in algebraic geometry.
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Table of Contents
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Chapters
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Introduction
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0. Background material
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1. The second reduction for $n$-folds in $\mathbb {P}^{2n - 1}$
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2. General formulae for threefolds in $\mathbb {P}^5$
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3. Nefness and bigness of $K_X + 2\mathcal {K}$
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4. Ampleness of $K_X + 2\mathcal {K}$
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5. Nefness and bigness of $K_X + \mathcal {K}$
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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 \(N \leq 2n-1\).
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
