An error was encountered while trying to add the item to the cart. Please try again.
The following link can be shared to navigate to this page. You can select the link to copy or click the 'Copy To Clipboard' button below.
Copy To Clipboard
Successfully Copied!
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 Click above image for expanded view 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 $N \leq 2n-1$.

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
• Request Review Copy
• Get Permissions
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 $N \leq 2n-1$.

• 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