Short sections of some bundles on the projective line
Zapiski Nauchnykh Seminarov POMI, Algebra and number theory. Part 3, Tome 490 (2020), pp. 124-141 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The paper concerns vector bundles on the projective line over the ring of integers. We deal with bundles of rank 2 obtained by means of a certain base change. The source bundle runs over the bundles with the trivial generic fiber an simple jumps. We compute the minimal degree of nonvaniching sections for bundles in question. Certain interesting phenomena are found out.
@article{ZNSL_2020_490_a7,
     author = {A. L. Smirnov and G. A. Strukov},
     title = {Short sections of some bundles on the projective line},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {124--141},
     year = {2020},
     volume = {490},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_490_a7/}
}
TY  - JOUR
AU  - A. L. Smirnov
AU  - G. A. Strukov
TI  - Short sections of some bundles on the projective line
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2020
SP  - 124
EP  - 141
VL  - 490
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2020_490_a7/
LA  - ru
ID  - ZNSL_2020_490_a7
ER  - 
%0 Journal Article
%A A. L. Smirnov
%A G. A. Strukov
%T Short sections of some bundles on the projective line
%J Zapiski Nauchnykh Seminarov POMI
%D 2020
%P 124-141
%V 490
%U http://geodesic.mathdoc.fr/item/ZNSL_2020_490_a7/
%G ru
%F ZNSL_2020_490_a7
A. L. Smirnov; G. A. Strukov. Short sections of some bundles on the projective line. Zapiski Nauchnykh Seminarov POMI, Algebra and number theory. Part 3, Tome 490 (2020), pp. 124-141. http://geodesic.mathdoc.fr/item/ZNSL_2020_490_a7/

[1] Ch. C. Hanna, “Subbundles of vector bundles on the projective line”, J. Algebra, 52:2 (1978), 322–327 | DOI | MR | Zbl

[2] G. A. Strukov, Vektornye rassloeniya na arifmeticheskikh mnogoobraziyakh, Diplomnaya rabota, Sankt-Peterburgskii gosudarstvennyi universitet, 2020

[3] R. Khartskhorn, Algebraicheskaya geometriya, Mir, M., 1981

[4] A. L. Smirnov, “Vektornye rassloeniya na $\mathbf{P}^1_{\mathbb{Z}}$ s prostymi podskokami”, Zap. nauchn. semin. POMI, 452, 2016, 202–217

[5] A. L. Smirnov, “On filtrations of vector bundles over $\mathbf{P}^1_{\mathbb{Z}}$. Arithmetic and Geometry”, London Math. Soc. Lect. Note Series, 420, Cambridge Univ. Press, 2015, 436–457 | MR | Zbl

[6] K. Okonek, M. Shnaider, Kh. Shpindler, Vektornye rassloeniya na kompleksnykh proektivnykh prostranstvakh, Mir, M., 1984

[7] S. S. Yakovenko, Vektornye $\mathbf{P}^1_{\mathbb{Z}}$-rassloeniya s obschim sloem $\mathcal O \oplus \mathcal O(1)$ i prostymi podskokami, Preprint POMI, 03, 2016

[8] A. L. Smirnov, S. S. Yakovenko, “Postroenie lineinoi filtratsii dlya rassloenii ranga $2$ na $\mathbf{P}^1_{\mathbb{Z}}$”, Matem. sbornik, 208 (2017), 111–128 | Zbl

[9] F. Griffits, Dzh. Kharris, Printsipy algebraicheskoi geometrii, v. 2, Mir, M., 1982 | MR

[10] Yu. I. Manin, Kubicheskie formy, Nauka, M., 1972