| Softcover ISBN: | 978-1-4704-2838-9 |
| Product Code: | MEMO/253/1209 |
| List Price: | $78.00 |
| MAA Member Price: | $70.20 |
| AMS Member Price: | $46.80 |
| Electronic ISBN: | 978-1-4704-4413-6 |
| Product Code: | MEMO/253/1209.E |
| List Price: | $78.00 |
| MAA Member Price: | $70.20 |
| AMS Member Price: | $46.80 |
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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 3-space. Among the bundles appearing in our classification one can find the Sasakura rank 3 vector bundle on the projective 4-space (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 \(n \leq 5\).
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Table of Contents
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Chapters
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Introduction
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1. Preliminaries
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2. Some general results
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3. The cases $c_1=4$ and $c_1 = 5$ on $\mathbb {P}^2$
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4. The case $c_1 = 4$, $c_2 = 5, 6$ on $\mathbb {P}^3$
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5. The case $c_1 = 4$, $c_2 = 7$ on $\mathbb {P}^3$
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6. The case $c_1 = 4$, $c_2 = 8$ on $\mathbb {P}^3$
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7. The case $c_1 = 4$, $5 \leq c_2 \leq 8$ on $\mathbb {P}^n$, $n \geq 4$
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A. The case $c_1 = 4$, $c_2 = 8$, $c_3 = 2$ on $\mathbb {P}^3$
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B. The case $c_1 = 4$, $c_2 = 8$, $c_3 = 4$ on $\mathbb {P}^3$
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Additional Material
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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 3-space. Among the bundles appearing in our classification one can find the Sasakura rank 3 vector bundle on the projective 4-space (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 \(n \leq 5\).
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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 $\mathbb {P}^3$
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5. The case $c_1 = 4$, $c_2 = 7$ on $\mathbb {P}^3$
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6. The case $c_1 = 4$, $c_2 = 8$ on $\mathbb {P}^3$
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7. The case $c_1 = 4$, $5 \leq c_2 \leq 8$ on $\mathbb {P}^n$, $n \geq 4$
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A. The case $c_1 = 4$, $c_2 = 8$, $c_3 = 2$ on $\mathbb {P}^3$
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B. The case $c_1 = 4$, $c_2 = 8$, $c_3 = 4$ on $\mathbb {P}^3$
