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Globally Generated Vector Bundles with Small $c_1$ on Projective Spaces

Cristian Anghel The Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest, Romania
Iustin Coandă The Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest, Romania
Nicolae Manolache The Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest, Romania
Available Formats:
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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AMS Member Price: $70.20 Click above image for expanded view Globally Generated Vector Bundles with Small$c_1$on Projective Spaces Cristian Anghel The Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest, Romania Iustin Coandă The Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest, Romania Nicolae Manolache The Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest, Romania Available Formats:  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 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$117.00 MAA Member Price: $105.30 AMS Member Price:$70.20
• Book Details

Memoirs of the American Mathematical Society
Volume: 2532018; 107 pp
MSC: 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 $n \leq 5$.

• 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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Review Copy – for reviewers who would like to review an AMS book
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Accessibility – to request an alternate format of an AMS title
Volume: 2532018; 107 pp
MSC: 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 $n \leq 5$.

• 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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