Geodesic
Bochner--Hartogs type extension theorem for roots and logarithms of holomorphic line bundles
Informatics and Automation, Analytic and geometric issues of complex analysis, Tome 279 (2012), pp. 269-287.

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We prove an extension theorem for roots and logarithms of holomorphic line bundles across strictly pseudoconcave boundaries: they extend in all cases except one, when the dimension and Morse index of a critical point is 2. In that case we give an explicit description of obstructions to the extension. 
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     title = {Bochner--Hartogs type extension theorem for roots and logarithms of holomorphic line bundles},
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S. Ivashkovich. Bochner--Hartogs type extension theorem for roots and logarithms of holomorphic line bundles. Informatics and Automation, Analytic and geometric issues of complex analysis, Tome 279 (2012), pp. 269-287. http://geodesic.mathdoc.fr/item/TRSPY_2012_279_a17/

[1] Bochner S., “A theorem on analytic continuation of functions in several variables”, Ann. Math. Ser. 2, 39:1 (1938), 14–19 | DOI | MR | Zbl

[2] Chern S. S., Complex manifolds, Univ. Chicago, Chicago, 1956

[3] Dethloff G.-E., “A new proof of a theorem of Grauert and Remmert by $L_2$-methods”, Math. Ann., 286 (1990), 129–142 | DOI | MR | Zbl

[4] Forstnerič F., “Stein domains in complex surfaces”, J. Geom. Anal., 13:1 (2003), 77–94 | DOI | MR | Zbl

[5] Frenkel J., “Cohomologie non abélienne et espaces fibrés”, Bull. Soc. math. France, 85 (1957), 135–220 | MR | Zbl

[6] Friedman R., Algebraic surfaces and holomorphic vector bundles, Universitext, Springer, New York, 1998 | DOI | MR

[7] Grauert H., Remmert R., “Komplexe Räume”, Math. Ann., 136 (1958), 245–318 | DOI | MR | Zbl

[8] Grauert H., Remmert R., Theorie der Steinschen Räume, Springer, Berlin, 1977 | MR

[9] Ivashkovich S. M., “Envelopes of holomorphy of some tube sets in $\mathbf C^2$ and the monodromy theorem”, Math. USSR. Izv., 19:1 (1982), 189–196 | DOI | MR | Zbl | Zbl

[10] Ivashkovich S. M., “The Hartogs-type extension theorem for meromorphic maps into compact Kähler manifolds”, Invent. math., 109 (1992), 47–54 | DOI | MR | Zbl

[11] Ivashkovich S. M., “Prodolzhenie analiticheskikh ob'ektov metodom Kartana–Tullena”, Kompleksnyi analiz i matematicheskaya fizika, In-t fiziki SO AN SSSR, Krasnoyarsk, 1988, 53–61 | MR

[12] Nemirovskii S. Yu., “Holomorphic functions and embedded real surfaces”, Math. Notes, 63 (1998), 527–532 | DOI | DOI | MR | Zbl

[13] Nishino T., Function theory in several complex variables, Transl. Math. Monogr., 193, Amer. Math. Soc., Providence, RI, 2001 | MR | Zbl

[14] Norguet F., Siu Y.-T., “Holomorphic convexity of spaces of analytic cycles”, Bull. Soc. math. France, 105 (1977), 191–223 | MR | Zbl

[15] Ohsawa T., “Nonexistence of real analytic Levi flat hypersurfaces in $\mathbb P^2$”, Nagoya Math. J., 158 (2000), 95–98 | MR | Zbl

[16] Royden H. L., “The extension of regular holomorphic maps”, Proc. Amer. Math. Soc., 43:2 (1974), 306–310 | DOI | MR | Zbl

[17] Siu Y.-T., “A Hartogs type extension theorem for coherent analytic sheaves”, Ann. Math. Ser. 2, 93 (1971), 166–188 | DOI | MR | Zbl

[18] Siu Y.-T., Techniques of extension of analytic objects, M. Dekker, New York, 1974 | MR | Zbl

[19] Siu Y.-T., Trautmann G., Gap-sheaves and extension of coherent analytic subsheaves, Lect. Notes. Math., 172, Springer, Berlin, 1971 | MR | Zbl

[20] Stolzenberg G., “Polynomially and rationally convex sets”, Acta math., 109 (1963), 259–289 | DOI | MR | Zbl