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Product Code:  MEMO/253/1209 
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Electronic ISBN:  9781470444136 
Product Code:  MEMO/253/1209.E 
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MAA Member Price:  $70.20 
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 253; 2018; 107 ppMSC: Primary 14;
The authors provide a complete classification of globally generated vector bundles with first Chern class \(c_1 \leq 5\) one the projective plane and with \(c_1 \leq 4\) on the projective \(n\)space for \(n \geq 3\). This reproves and extends, in a systematic manner, previous results obtained for \(c_1 \leq 2\) by Sierra and Ugaglia [J. Pure Appl. Algebra 213 (2009), 2141–2146], and for \(c_1 = 3\) by Anghel and Manolache [Math. Nachr. 286 (2013), 1407–1423] and, independently, by Sierra and Ugaglia [J. Pure Appl. Algebra 218 (2014), 174–180]. It turns out that the case \(c_1 = 4\) is much more involved than the previous cases, especially on the projective 3space. Among the bundles appearing in our classification one can find the Sasakura rank 3 vector bundle on the projective 4space (conveniently twisted). The authors also propose a conjecture concerning the classification of globally generated vector bundles with \(c_1 \leq n  1\) on the projective \(n\)space. They verify the conjecture for \(n \leq 5\).

Table of Contents

Chapters

Introduction

1. Preliminaries

2. Some general results

3. The cases $c_1=4$ and $c_1 = 5$ on $\mathbb {P}^2$

4. The case $c_1 = 4$, $c_2 = 5, 6$ on $\mathbb {P}^3$

5. The case $c_1 = 4$, $c_2 = 7$ on $\mathbb {P}^3$

6. The case $c_1 = 4$, $c_2 = 8$ on $\mathbb {P}^3$

7. The case $c_1 = 4$, $5 \leq c_2 \leq 8$ on $\mathbb {P}^n$, $n \geq 4$

A. The case $c_1 = 4$, $c_2 = 8$, $c_3 = 2$ on $\mathbb {P}^3$

B. The case $c_1 = 4$, $c_2 = 8$, $c_3 = 4$ on $\mathbb {P}^3$


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The authors provide a complete classification of globally generated vector bundles with first Chern class \(c_1 \leq 5\) one the projective plane and with \(c_1 \leq 4\) on the projective \(n\)space for \(n \geq 3\). This reproves and extends, in a systematic manner, previous results obtained for \(c_1 \leq 2\) by Sierra and Ugaglia [J. Pure Appl. Algebra 213 (2009), 2141–2146], and for \(c_1 = 3\) by Anghel and Manolache [Math. Nachr. 286 (2013), 1407–1423] and, independently, by Sierra and Ugaglia [J. Pure Appl. Algebra 218 (2014), 174–180]. It turns out that the case \(c_1 = 4\) is much more involved than the previous cases, especially on the projective 3space. Among the bundles appearing in our classification one can find the Sasakura rank 3 vector bundle on the projective 4space (conveniently twisted). The authors also propose a conjecture concerning the classification of globally generated vector bundles with \(c_1 \leq n  1\) on the projective \(n\)space. They verify the conjecture for \(n \leq 5\).

Chapters

Introduction

1. Preliminaries

2. Some general results

3. The cases $c_1=4$ and $c_1 = 5$ on $\mathbb {P}^2$

4. The case $c_1 = 4$, $c_2 = 5, 6$ on $\mathbb {P}^3$

5. The case $c_1 = 4$, $c_2 = 7$ on $\mathbb {P}^3$

6. The case $c_1 = 4$, $c_2 = 8$ on $\mathbb {P}^3$

7. The case $c_1 = 4$, $5 \leq c_2 \leq 8$ on $\mathbb {P}^n$, $n \geq 4$

A. The case $c_1 = 4$, $c_2 = 8$, $c_3 = 2$ on $\mathbb {P}^3$

B. The case $c_1 = 4$, $c_2 = 8$, $c_3 = 4$ on $\mathbb {P}^3$