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Izv. RAN. Ser. Mat., 2001, Volume 65, Issue 1, Pages 133–196 (Mi izv324)  

This article is cited in 2 scientific papers (total in 3 papers)

Non-abelian analogues of Abel's theorem

A. N. Tyurin

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: Vafa [29] extended a version of mirror symmetry to pairs consisting of a Calabi–Yau manifold and a fixed vector bundle on it. In [30] he considered the mathematical meaning of this extension. In this paper we prove the main facts concerning the geometry of vector bundles on Calabi–Yau manifolds and describe all constructions that enable us to embed them in the general context of modern physical concepts.

DOI: https://doi.org/10.4213/im324

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English version:
Izvestiya: Mathematics, 2001, 65:1, 123–180

Bibliographic databases:

MSC: 14J32, 53C15
Received: 16.05.2000

Citation: A. N. Tyurin, “Non-abelian analogues of Abel's theorem”, Izv. RAN. Ser. Mat., 65:1 (2001), 133–196; Izv. Math., 65:1 (2001), 123–180

Citation in format AMSBIB
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\by A.~N.~Tyurin
\paper Non-abelian analogues of Abel's theorem
\jour Izv. RAN. Ser. Mat.
\yr 2001
\vol 65
\issue 1
\pages 133--196
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\crossref{https://doi.org/10.4213/im324}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1829408}
\zmath{https://zbmath.org/?q=an:1015.14020}
\transl
\jour Izv. Math.
\yr 2001
\vol 65
\issue 1
\pages 123--180
\crossref{https://doi.org/10.1070/im2001v065n01ABEH000324}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-7244229517}


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    This publication is cited in the following articles:
    1. F. A. Bogomolov, A. L. Gorodentsev, V. A. Iskovskikh, Yu. I. Manin, V. V. Nikulin, D. O. Orlov, A. N. Parshin, V. Ya. Pidstrigach, A. S. Tikhomirov, N. A. Tyurin, I. R. Shafarevich, “Andrei Nikolaevich Tyurin (obituary)”, Russian Math. Surveys, 58:3 (2003), 597–605  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. Chiantini L., Madonna C., “A splitting criterion for rank 2 bundles on a general sextic threefold”, Internat. J. Math., 15:4 (2004), 341–359  crossref  mathscinet  zmath  isi  elib  scopus
    3. Morrison D.R., Walcher J., “D-branes and normal functions”, Adv. Theor. Math. Phys., 13:2 (2009), 553–598  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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