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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
Globally Generated Vector Bundles with Small $c_1$ on Projective Spaces
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
eBook 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
Softcover ISBN:  978-1-4704-2838-9
eBook: ISBN:  978-1-4704-4413-6
Product Code:  MEMO/253/1209.B
List Price: $156.00 $117.00
MAA Member Price: $140.40 $105.30
AMS Member Price: $93.60 $70.20
Globally Generated Vector Bundles with Small $c_1$ on Projective Spaces
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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
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
eBook 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
Softcover ISBN:  978-1-4704-2838-9
eBook ISBN:  978-1-4704-4413-6
Product Code:  MEMO/253/1209.B
List Price: $156.00 $117.00
MAA Member Price: $140.40 $105.30
AMS Member Price: $93.60 $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 \(n \leq 5\).

  • 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 $\mathbb {P}^3$
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    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 $\mathbb {P}^3$
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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