**Memoirs of the American Mathematical Society**

2018;
107 pp;
Softcover

MSC: Primary 14;

**Print ISBN: 978-1-4704-2838-9
Product Code: MEMO/253/1209**

List Price: $78.00

AMS Member Price: $46.80

MAA Member Price: $70.20

**Electronic ISBN: 978-1-4704-4413-6
Product Code: MEMO/253/1209.E**

List Price: $78.00

AMS Member Price: $46.80

MAA Member Price: $70.20

# Globally Generated Vector Bundles with Small \(c_{1}\) on Projective Spaces

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*Cristian Anghel; Iustin Coandă; Nicolae Manolache*

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

# Table of Contents

## Globally Generated Vector Bundles with Small $c_{1}$ on Projective Spaces

- Cover Cover11
- Title page i2
- Introduction 18
- Chapter 1. Preliminaries 714
- Chapter 2. Some general results 2128
- Chapter 3. The cases 𝑐₁=4 and 𝑐₁=5 on ℙ² 2936
- Chapter 4. The case 𝑐₁=4, 𝑐₂=5,6 on ℙ³ 3744
- Chapter 5. The case 𝑐₁=4, 𝑐₂=7 on ℙ³ 4350
- Chapter 6. The case 𝑐₁=4, 𝑐₂=8 on ℙ³ 4956
- Chapter 7. The case 𝑐₁=4, 5≤𝑐₂≤8 on ℙⁿ, 𝕟≥4 6976
- Appendix A. The case 𝑐₁=4, 𝑐₂=8, 𝑐₃=2 on ℙ³ 8592
- Appendix B. The case 𝑐₁=4, 𝑐₂=8, 𝑐₃=4 on ℙ³ 95102
- Bibliography 105112
- Back Cover Back Cover1120