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OverviewThe 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 DetailsAuthor: Cristian Anghel , Iustin Coanda , Nicolae ManolachePublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.185kg ISBN: 9781470428389ISBN 10: 1470428385 Pages: 101 Publication Date: 30 June 2018 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Temporarily unavailable  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 ContentsIntroduction 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.ReviewsAuthor InformationCristian 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. Tab Content 6Author Website:Countries AvailableAll regions |
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