Globally Generated Vector Bundles with Small $c_1$ on Projective Spaces
Author:   Cristian Anghel ,  Iustin Coanda ,  Nicolae Manolache
Publisher:   American Mathematical Society
ISBN:  

9781470428389


Pages:   101
Publication Date:   30 June 2018
Format:   Paperback
Availability:   Temporarily unavailable   Availability explained
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Globally Generated Vector Bundles with Small $c_1$ on Projective Spaces


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Overview

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 $n \leq 5$.

Full Product Details

Author:   Cristian Anghel ,  Iustin Coanda ,  Nicolae Manolache
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Weight:   0.185kg
ISBN:  

9781470428389


ISBN 10:   1470428385
Pages:   101
Publication Date:   30 June 2018
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Temporarily unavailable   Availability explained
The supplier advises that this item is temporarily unavailable. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out to you.

Table of Contents

Introduction Acknowledgements Preliminaries Some general results The cases $c_1=4$ and $c_1 = 5$ on ${\mathbb P}^2$ The case $c_1 = 4$, $c_2 = 5, 6$ on ${\mathbb P}^3$ The case $c_1 = 4$, $c_2 = 7$ on ${\mathbb P}^3$ The case $c_1 = 4$, $c_2 = 8$ on ${\mathbb P}^3$ The case $c_1 = 4$, $5 \leq c_2 \leq 8$ on ${\mathbb P}^n$, $n \geq 4$ Appendix A. The case $c_1 = 4$, $c_2 = 8$, $c_3 = 2$ on ${\mathbb P}^3$ Appendix B. The case $c_1 = 4$, $c_2 = 8$, $c_3 = 4$ on ${\mathbb P}^3$ Bibliography.

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Cristian Anghel, The Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest, Romania. Iustin Coanda, 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.

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