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Uspekhi Mat. Nauk, 1997, Volume 52, Issue 1(313), Pages 149–224 (Mi umn808)  

This article is cited in 16 scientific papers (total in 16 papers)

Secants of Abelian varieties, theta functions, and soliton equations

I. A. Taimanov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

DOI: https://doi.org/10.4213/rm808

Full text: PDF file (733 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 1997, 52:1, 147–218

Bibliographic databases:

UDC: 512.742+517.957
MSC: 35Q51, 14K25, 14H40
Received: 26.05.1996

Citation: I. A. Taimanov, “Secants of Abelian varieties, theta functions, and soliton equations”, Uspekhi Mat. Nauk, 52:1(313) (1997), 149–224; Russian Math. Surveys, 52:1 (1997), 147–218

Citation in format AMSBIB
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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. Mironov A.E., “Commutative rings of differential operators connected with two-dimensional Abelian varieties”, Siberian Math. J., 41:6 (2000), 1148–1161  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    2. Karassiov V.P., “Symmetry approach to reveal hidden coherent structures in quantum optics. General outlook and examples”, Journal of Russian Laser Research, 21:4 (2000), 370–410  crossref  isi  elib  scopus  scopus
    3. Mironov A.E., “Real commuting differential operators connected with two-dimensional abelian varieties”, Siberian Math. J., 43:1 (2002), 97–113  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    4. Mironov A.E., “On nonlinear equations integrable in theta functions of nonprincipally polarized abelian varieties”, Siberian Math. J., 42:1 (2001), 99–107  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    5. Kalnins E.G., Karassiov V.P., “Polynomial Lie algebras $\hat E_{R_1}^{\mathcal P}(u(n);(m))$ in nonlinear models of quantum optics: basic ideas and cluster dynamics in the Heisenberg picture”, Journal of Russian Laser Research, 24:5 (2003), 402–424  crossref  isi  elib  scopus  scopus
    6. Karassiov V.P., “Dual algebraic pairs and polynomial Lie algebras in quantum physics: Foundations and geometric aspects”, Proceedings of the Workshop on Contemporary Geometry and Related Topics, 2004, 285–300  crossref  mathscinet  zmath  isi
    7. Krichever I., “A characterization of Prym varieties”, Int. Math. Res. Not., 2006, 81476, 36 pp.  crossref  mathscinet  zmath  isi  scopus  scopus
    8. V. M. Buchstaber, I. M. Krichever, “Integrable equations, addition theorems, and the Riemann–Schottky problem”, Russian Math. Surveys, 61:1 (2006), 19–78  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    9. Tu Ming-Hsien, “On the BKP hierarchy: additional symmetries, Fay identity and Adler-Shiota-van Moerbeke formula”, Lett. Math. Phys., 81:2 (2007), 93–105  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    10. I. M. Krichever, “Abelian solutions of the soliton equations and Riemann–Schottky problems”, Russian Math. Surveys, 63:6 (2008), 1011–1022  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    11. Previato E., “Multivariable Burchnall-Chaundy theory”, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 366:1867 (2008), 1155–1177  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    12. D. V. Egorov, “Theta functions on the Kodaira–Thurston manifold”, Siberian Math. J., 50:2 (2009), 253–260  mathnet  crossref  mathscinet  isi  elib  elib
    13. D. V. Egorov, “Theta functions on $T^2$-bundles over $T^2$ with the zero Euler class”, Siberian Math. J., 50:4 (2009), 647–657  mathnet  crossref  mathscinet  isi  elib  elib
    14. Grushevsky S., “Geometry of A(g) and Its Compactifications”, Algebraic Geometry, Proceedings of Symposia in Pure Mathematics, 80, no. 1- 2, 2009, 193–234  crossref  mathscinet  zmath  isi
    15. Kharchev S. Zabrodin A., “Theta vocabulary II. Multidimensional case”, J. Geom. Phys., 104 (2016), 112–120  crossref  mathscinet  zmath  isi  elib  scopus
    16. Andrew N. W. Hone, Theodoros E. Kouloukas, Chloe Ward, “On Reductions of the Hirota–Miwa Equation”, SIGMA, 13 (2017), 057, 17 pp.  mathnet  crossref
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