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 Izv. Akad. Nauk SSSR Ser. Mat., 1980, Volume 44, Issue 1, Pages 219–232 (Mi izv1644)

A. S. Tikhomirov

Abstract: 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.

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English version:
Mathematics of the USSR-Izvestiya, 1981, 16:1, 207–220

Bibliographic databases:

UDC: 513.6
MSC: Primary 14D20; Secondary 14M99

Citation: A. S. Tikhomirov, “A four-dimensional bundle of quadrics, and a monad”, Izv. Akad. Nauk SSSR Ser. Mat., 44:1 (1980), 219–232; Math. USSR-Izv., 16:1 (1981), 207–220

Citation in format AMSBIB
\Bibitem{Tik80} \by A.~S.~Tikhomirov \paper A four-dimensional bundle of quadrics, and a~monad \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1980 \vol 44 \issue 1 \pages 219--232 \mathnet{http://mi.mathnet.ru/izv1644} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=563793} \zmath{https://zbmath.org/?q=an:0465.14003|0432.14009} \transl \jour Math. USSR-Izv. \yr 1981 \vol 16 \issue 1 \pages 207--220 \crossref{https://doi.org/10.1070/IM1981v016n01ABEH001291} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1981LP24600011}