Geodesic
The Hartogs extension phenomenon in almost homogeneous algebraic varieties
Sbornik. Mathematics, Tome 213 (2022) no. 12, pp. 1715-1739 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the Hartogs extension phenomenon in noncompact almost homogeneous algebraic varieties, and we prove a cohomological and a weight criterion for the Hartogs phenomenon. In the case of spherical varieties we prove a criterion for the Hartogs phenomenon in terms of coloured fans. Bibliography: 28 titles.
Keywords: Hartogs phenomenon, holomorphic extension, almost homogeneous algebraic variety, spherical variety. 
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S. V. Feklistov. The Hartogs extension phenomenon in almost homogeneous algebraic varieties. Sbornik. Mathematics, Tome 213 (2022) no. 12, pp. 1715-1739. http://geodesic.mathdoc.fr/item/SM_2022_213_12_a5/

[1] D. N. Akhiezer, Lie group actions in complex analysis, Aspects Math., E27, Friedr. Vieweg Sohn, Braunschweig, 1995, viii+201 pp. | DOI | MR | Zbl

[2] M. Andersson and H. Samuelsson, Koppelman formulas and the $\bar{\partial}$-equation on an analytic space, Institut Mittag-Leffler preprint series, 2008, 31 pp.

[3] A. Andreotti and H. Grauert, “Théorèmes de finitude pour la cohomologie des espaces complexes”, Bull. Soc. Math. France, 90 (1962), 193–259 | DOI | MR | Zbl

[4] A. Andreotti and C. D. Hill, “E. E. Levi convexity and the Hans Lewy problem. I. Reduction to vanishing theorems”, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3), 26:2 (1972), 325–363 | MR | Zbl

[5] A. Andreotti and E. Vesentini, “Carleman estimates for the Laplace-Beltrami equation on complex manifolds”, Inst. Hautes Études Sci. Publ. Math., 25 (1965), 81–130 | DOI | MR | Zbl

[6] C. Bănică and O. Stănăşilă, Algebraic methods in the global theory of complex spaces, Editura Academiei, Bucuresti; John Wiley Sons, Ltd., London–New York–Sydney, 1976, 296 pp. | MR | Zbl

[7] G. E. Bredon, Sheaf theory, Grad. Texts in Math., 170, 2nd ed., Springer-Verlag, New York, 1997, xii+502 pp. | DOI | MR | Zbl

[8] M. Brion, “Une extension du théorème de Borel-Weil”, Math. Ann., 286:4 (1990), 655–660 | DOI | MR | Zbl

[9] M. Brion, “Introduction to actions of algebraic groups”, Les Cours du CIRM, 1:1 (2010), 1–22 | DOI

[10] M. Colţoiu and J. Ruppenthal, “On Hartogs' extension theorem on $(n - 1)$-complete complex spaces”, J. Reine Angew. Math., 2009:637 (2009), 41–47 | DOI | MR | Zbl

[11] R. J. Dwilewicz, “Holomorphic extensions in complex fiber bundles”, J. Math. Anal. Appl., 322:2 (2006), 556–565 | DOI | MR | Zbl

[12] S. Feklistov and A. Shchuplev, “The Hartogs extension phenomenon in toric varieties”, J. Geom. Anal., 31:12 (2021), 12034–12052 | DOI | MR | Zbl

[13] J. Gandini, “Embeddings of spherical homogeneous spaces”, Acta Math. Sin. (Engl. Ser.), 34:3 (2018), 299–340 | DOI | MR | Zbl

[14] Complex analysis — several variables – 7, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 74, eds. H. Grauert, Th. Peternell, R. Remmert and R. V. Gamkrelidze, VINITI, Moscow, 1996, 472 pp. ; English transl., Several complex variables VII. Sheaf-theoretical methods in complex analysis, Encyclopaedia Math. Sci., 74, eds. H. Grauert, Th. Peternell and R. Remmert, Springer-Verlag, Berlin, 1994, vi+369 pp. | MR | Zbl | DOI

[15] R. Hartshorne, Algebraic geometry, Grad. Texts in Math., 52, Springer-Verlag, New York–Heidelberg, 1977, xvi+496 pp. | DOI | MR | Zbl

[16] R. Harvey, “The theory of hyperfunctions on totally real subsets of a complex manifold with applications to extension problems”, Amer. J. Math., 91:4 (1969), 853–873 | DOI | MR | Zbl

[17] J. E. Humphreys, Linear algebraic groups, Grad. Texts in Math., 21, Corr. 5th print., Springer-Verlag, New York–Heidelberg, 1998, xiv+247 pp. | DOI | MR | Zbl

[18] M. A. Marciniak, Holomorphic extensions in toric varieties, Thesis (Ph.D.), Missouri Univ. of Science and Technology, Missouri, 2009, 147 pp. | MR

[19] M. A. Marciniak, “Holomorphic extensions in smooth toric surfaces”, J. Geom. Anal., 22:4 (2012), 911–933 | DOI | MR | Zbl

[20] J. Merker and E. Porten, “The Hartogs extension theorem on $(n-1)$-complete complex spaces”, J. Reine Angew. Math., 2009:637 (2009), 23–39 | DOI | MR | Zbl

[21] G. Peschke, “The theory of ends”, Nieuw Arch. Wisk. (4), 8:1 (1990), 1–12 | MR | Zbl

[22] H. Rossi, “Vector fields on analytic spaces”, Ann. of Math. (2), 78:3 (1963), 455–467 | DOI | MR | Zbl

[23] J.-P. Serre, “Quelques problèmes globaux relatifs aux variétés de Stein”, Colloque sur les fonctions de plusieurs variables (Bruxelles 1953), Georges Thone, Liège; Masson Cie, Paris, 1953, 57–68 | MR | Zbl

[24] M. R. Sepanski, Compact Lie groups, Grad. Texts in Math., 235, Springer, New York, 2007, xiv+198 pp. | DOI | MR | Zbl

[25] H. Sumihiro, “Equivariant completion”, J. Math. Kyoto Univ., 14:1 (1974), 1–28 | DOI | MR | Zbl

[26] N. Øvrelid and S. Vassiliadou, “Hartogs extension theorems on Stein spaces”, J. Geom. Anal., 20:4 (2010), 817–836 | DOI | MR | Zbl

[27] V. Vîjîitu, “On Hartogs' extension”, Ann. Mat. Pura Appl. (4), 201:1 (2022), 487–498 | DOI | MR | Zbl

[28] D. A. Timashev, Homogeneous spaces and equivariant embeddings, Encyclopaedia Math. Sci., 138, Invariant Theory and Algebraic Transformation Groups, 8, Springer, Heidelberg, 2011, xxii+253 pp. | DOI | MR | Zbl