A four-dimensional bundle of quadrics, and a~monad

A. S. Tikhomirov

Izvestiya. Mathematics , Tome 16 (1981) no. 1, pp. 207-220

Résumé

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.