Globally generated vector bundles with small c1 on projective spaces

著者

    • Anghel, Cristian
    • Coanda, Iustin
    • Manolache, Nicolae

書誌事項

Globally generated vector bundles with small c1 on projective spaces

Cristian Anghel, Iustin Coanda, Nicolae Manolache

(Memoirs of the American Mathematical Society, no. 1209)

American Mathematical Society, c2018

大学図書館所蔵 件 / 9

この図書・雑誌をさがす

注記

Includes bibliographical references

May 2018, volume 253, number 1209 (fourth of 7 numbers)

内容説明・目次

内容説明

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 $n \leq 5$.

目次

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.

「Nielsen BookData」 より

関連文献: 1件中  1-1を表示

詳細情報

ページトップへ