Globally Generated Vector Bundles with Small $c_1$ on Projective Spaces (eBook)

Anghel C Viorel (Autor)

eBook Download: PDF

107 Seiten
American Mathematical Society (Verlag)
978-1-4704-4413-6 (ISBN)

Infos

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 $n /leq 5$.

Produkt-Details

• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• ISBN-10: 1-4704-4413-5 / 1470444135
• ISBN-13: 978-1-4704-4413-6 / 9781470444136