Intersections of analytic sets with linear subspaces
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 17 (1990) no. 2, pp. 227-271. 
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     author = {Tworzewski, Piotr},
     title = {Intersections of analytic sets with linear subspaces},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {227--271},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 17},
     number = {2},
     year = {1990},
     mrnumber = {1076253},
     zbl = {0717.32006},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1990_4_17_2_227_0/}
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Tworzewski, Piotr. Intersections of analytic sets with linear subspaces. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 17 (1990) no. 2, pp. 227-271. http://www.numdam.org/item/ASNSP_1990_4_17_2_227_0/

[1] J. Bochnak - W. Kucharz, Local algebraicity of analytic sets, J. reine angew. Math., 352 (1984), pp. 1-14. | MR | Zbl

[2] S. Bochner - W.T. Martin, Several complex variables, Princeton, 1948. | MR | Zbl

[3] C. Chevalley, Introduction to the theory of algebraic functions of one variable, AMS, New York, 1951. | MR | Zbl

[4] J. Dieudonné, Fundations of modern analysis, New York, 1960. | MR | Zbl

[5] E. Fortuna - S. Lojasiewicz, Sur L'algébricité des ensembles analytiques complexes, J. reine angew. Math., 329 (1981), pp. 215-220. | MR | Zbl

[6] E. Fortuna - S. Lojasiewicz - M. Raimondo, Algébricité de germes analytiques, Dipartimento di Matematica, Università di Pisa, 142 (1986), pp. 1-14. | MR

[7] P. Griffiths - J. Harris, Principles of Algebraic Geometry, Harvard University, 1978. | MR

[8] L. Gruman, The are of analytic varieties in Cn, Math. Scand., 41 (1977), pp. 365-397. | MR | Zbl

[9] L. Gruman, La géométrie globale des ensembles analytiques dans Cn, Seminaire P. Lelong, H. Skoda 1978-79, pp. 90-99. | MR | Zbl

[10] R.C. Gunning - H. Rossi, Analytic functions of several complex variables, Englewood Cliffs, N.J., 1965. | MR | Zbl

[11] M. Herve, Several complex variables, local theory, Oxford University Press, Bombay, 1963. | Zbl

[12] M. Jarnicki - P. Tworzewski, A note on holomorphic functions with polynomial growth, Osnabrücker Shriften zur Mathematik, 67 (1983), pp. 1-12.

[13] M. Koronevskij, Kriterij ratsional'nosti i psevdoratsional'nosti funktsij, Teorija funktsij i funktsional'nyj analiz, Prilozhenija, 18 (1973), pp. 91-102.

[14] F. Leja, Teoria funckji analitycznych, Warszawa, 1957.

[15] S. Lojasiewicz, Ensembles semi-analytiques, I.H.E.S., Bures-sur-Yvette, 1965.

[16] R.E. Molzon, Potential theory on complex projective space: application to characterization of pluripolar sets and growth of analytic varieties, Ill. J. Math., 28 (1984), pp. 103-119. | Zbl

[17] R.E. Molzon - B. Shiffman - N. Sibony, Average growth estimates for hyperplane sections of entire analytic sets, Math. Ann., 257 (1981), pp. 43-59. | Zbl

[18] D. Mumford, Algebraic Geometry I, Springer Verlag, 1976. | Zbl

[19] W. Rudin, A geometric criterion for algebraic varieties, J. Math. Mech., 17, 7 (1968), pp. 671-683. | Zbl

[20] K. Rusek, A geometric criterion for analytic sets of dimension one to be algebraic, Bull. Ac. Pol. Math., XXIX, 3-4 (1981), pp. 127-130. | Zbl

[21] A. Sadullaev, Kriterij algebraichnosti analiticheskikh mnozhestv, Sbornik o golomorfnykh funktsijakh mnogikh kompleksnykh peremennykh, Krasnojarsk, 1976, pp. 107-122.

[22] J.P. Serre, Géométrie algébrique et géométrie analytique, Ann. Inst. Fourier, Grenoble VI (1955-56), pp. 1-42. | Numdam | MR | Zbl

[23] N. Sibony - P.M. Wong, Some results on global analytic sets, Seminaire P. Lelong, H. Skoda, 1978-79, pp. 221-237. | MR | Zbl

[24] J. Siciak, A note on rational functions of several complex variables, Ann. Polon. Math., 12 (1962), pp. 139-142. | MR | Zbl

[25] J. Siciak, Extremal Plurisubharmonic Functions and Capacities in Cn, Sophia University, Tokyo, 1982. | Zbl

[26] W. Stoll, The growth of the area of a transcendental analytic set I, II, Math. Ann., 156 (1964), pp. 47-78, 144-170. | MR | Zbl

[27] W. Stoll, Invariant forms on Grassmann manifolds, Princeton, 1977. | MR | Zbl

[28] P. Tworzewski, Some conditions for the algebraicity of analytic sets, Bull. Ac. Pol. Math. XXIX, 11-12 (1981), pp. 545-548. | MR | Zbl

[29] P. Tworzewski - T. Winiarski, Analytic sets with proper projections, J. reine angew. Math., 337 (1982), pp. 68-76. | MR | Zbl

[30] P. Tworzewski - T. Winiarski, Limits of algebraic sets of bounded degree, Univ. lagellonicae Acta Math., XXIV (1984), pp. 151-153. | MR | Zbl

[31] H. Whitney, Complex Analytic Varieties, Princeton, 1972. | MR

[32] T. Winiarski, Continuity of total number of intersection, Ann. Polon. Math. XLVII (1986), pp. 155-178. | MR | Zbl