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Izv. Akad. Nauk SSSR Ser. Mat., 1989, Volume 53, Issue 2, Pages 363–378 (Mi izv1245)  

This article is cited in 3 scientific papers (total in 3 papers)

An existence theorem for exceptional bundles on $\mathrm K3$ surfaces

S. A. Kuleshov


Abstract: Discrete invariants of exceptional bundles on a $\mathrm K3$ surface $S$ obey the equation $c_1^2-2r(r-c_2+c_1^2/2)=-2$. In this paper it is proved that if the triple $(r,c_1,c_2)\in\mathbf Z\times\operatorname{Pic}(S)\times\mathbf Z$ satisfies this equation, then there exists an exceptional bundle $E$ on $S$ for which $r(E)=r$, $c_1(E)=c_1$ and $c_2(E)=c_2$ (modulo numerical equivalence). In addition, methods of constructing exceptional bundles on a $\mathrm K3$ surface are indicated.
Bibliography: 10 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1990, 34:2, 373–388

Bibliographic databases:

UDC: 512.723
MSC: Primary 14J28; Secondary 14J05, 14J10
Received: 26.04.1988

Citation: S. A. Kuleshov, “An existence theorem for exceptional bundles on $\mathrm K3$ surfaces”, Izv. Akad. Nauk SSSR Ser. Mat., 53:2 (1989), 363–378; Math. USSR-Izv., 34:2 (1990), 373–388

Citation in format AMSBIB
\Bibitem{Kul89}
\by S.~A.~Kuleshov
\paper An existence theorem for exceptional bundles on $\mathrm K3$ surfaces
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1989
\vol 53
\issue 2
\pages 363--378
\mathnet{http://mi.mathnet.ru/izv1245}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=998301}
\zmath{https://zbmath.org/?q=an:0706.14009}
\transl
\jour Math. USSR-Izv.
\yr 1990
\vol 34
\issue 2
\pages 373--388
\crossref{https://doi.org/10.1070/IM1990v034n02ABEH001316}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. Zube, “Exceptional vector bundles on Enriques surfaces”, Math. Notes, 61:6 (1997), 693–699  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. L. Costa, R.M. Miró-Roig, “A counterexample to a conjecture due to Douglas, Reinbacher and Yau”, Journal of Geometry and Physics, 57:11 (2007), 2229  crossref
    3. Bayer A., Bridgeland T., “Derived automorphism groups of K3 surfaces of Picard rank $1$”, Duke Math. J., 166:1 (2017), 75–124  crossref  mathscinet  zmath  isi  scopus
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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