Geodesic
A four-dimensional bundle of quadrics, and a monad
Izvestiya. Mathematics, Tome 16 (1981) no. 1, pp. 207-220 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper the author constructs a regular mapping $f$ of the variety of moduli of stable two-dimensional vector bundles $\mathscr F$ on $P^3$ with Chern classes $c_1(\mathscr F)=0$ and $c_2(\mathscr F)=n$ which satisfy $h^1(P^3,\mathscr F(-2))=0$, into the variety of classes of four-dimensional bundles of quadrics (whose base is the Grassmannian $G(1,3)$) in $P^{n-1}$. He proves that $f$ is an embedding. For the proof he constructs a monad on $P^3$ for the class of $f(\mathscr F)$, such that the cohomology sheaf of the monad is isomorphic to the vector bundle $\mathscr F$. Bibliography: 4 titles. 
@article{IM2_1981_16_1_a10,
     author = {A. S. Tikhomirov},
     title = {A four-dimensional bundle of quadrics, and a~monad},
     journal = {Izvestiya. Mathematics},
     pages = {207--220},
     year = {1981},
     volume = {16},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1981_16_1_a10/}
}
TY  - JOUR
AU  - A. S. Tikhomirov
TI  - A four-dimensional bundle of quadrics, and a monad
JO  - Izvestiya. Mathematics
PY  - 1981
SP  - 207
EP  - 220
VL  - 16
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/IM2_1981_16_1_a10/
LA  - en
ID  - IM2_1981_16_1_a10
ER  - 
%0 Journal Article
%A A. S. Tikhomirov
%T A four-dimensional bundle of quadrics, and a monad
%J Izvestiya. Mathematics
%D 1981
%P 207-220
%V 16
%N 1
%U http://geodesic.mathdoc.fr/item/IM2_1981_16_1_a10/
%G en
%F IM2_1981_16_1_a10
A. S. Tikhomirov. A four-dimensional bundle of quadrics, and a monad. Izvestiya. Mathematics, Tome 16 (1981) no. 1, pp. 207-220. http://geodesic.mathdoc.fr/item/IM2_1981_16_1_a10/

[1] Horrocks G., “Vector bundles on the punctured spectrum of local ring”, Proc. London Math. Soc., 14 (1964), 689–714 | DOI | MR

[2] Barth W., Hulek K., “Monads and moduli of vector bundles”, Manuscripta math., 25 (1978), 323–347 | DOI | MR | Zbl

[3] Barth W., “Moduli of stable vector bundles on the projective plane”, Inventiones math., 42 (1977), 63–91 | DOI | MR | Zbl

[4] Barth W., “Some properties of stable rank-2 vector bundles on $P_n$”, Math. Ann., 226 (1977), 125–150 | DOI | MR | Zbl