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Izv. RAN. Ser. Mat., 1992, Volume 56, Issue 1, Pages 38–74 (Mi izv957)  

This article is cited in 2 scientific papers (total in 2 papers)

Semistable sheaves on a two-dimensional quadric, and Kronecker modules

B. V. Karpov


Abstract: The author studies the connection between semistable sheaves on $\mathbf P^1\times\mathbf P^1$ that are represented as the cokernel of an injective morphism $E_1\otimes\mathbf C^m\to E_2\otimes\mathbf C^n$, where $E_1$ and $E_2$ are exceptional bundles, and semistable Kronecker modules $\mathbf C^m\otimes\operatorname{Hom}(E_1,E_2)^*\to\mathbf C^n$. He obtains sufficient conditions on the topological invariants of the sheaves for the moduli space of semistable sheaves and the corresponding Kronecker moduli space to coincide. This gives important geometric information concerning the moduli spaces of the bundles.

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English version:
Russian Academy of Sciences. Izvestiya Mathematics, 1993, 40:1, 33–66

Bibliographic databases:

UDC: 512.723
MSC: Primary 14J60, 14J26; Secondary 14F05, 14J10
Received: 16.04.1991

Citation: B. V. Karpov, “Semistable sheaves on a two-dimensional quadric, and Kronecker modules”, Izv. RAN. Ser. Mat., 56:1 (1992), 38–74; Russian Acad. Sci. Izv. Math., 40:1 (1993), 33–66

Citation in format AMSBIB
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\by B.~V.~Karpov
\paper Semistable sheaves on a two-dimensional quadric, and Kronecker modules
\jour Izv. RAN. Ser. Mat.
\yr 1992
\vol 56
\issue 1
\pages 38--74
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\zmath{https://zbmath.org/?q=an:0785.14006}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1993IzMat..40...33K}
\transl
\jour Russian Acad. Sci. Izv. Math.
\yr 1993
\vol 40
\issue 1
\pages 33--66
\crossref{https://doi.org/10.1070/IM1993v040n01ABEH001860}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1993LD16700002}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. A. Kuleshov, “On moduli spaces for stable bundles on quadrics”, Math. Notes, 62:6 (1997), 707–725  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. A. L. Gorodentsev, S. A. Kuleshov, “Helix theory”, Mosc. Math. J., 4:2 (2004), 377–440  mathnet  crossref  mathscinet  zmath
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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