Intersections of analytic sets with linear subspaces
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 17 (1990) no. 2, p. 227-271
@article{ASNSP_1990_4_17_2_227_0,
     author = {Tworzewski, Piotr},
     title = {Intersections of analytic sets with linear subspaces},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 17},
     number = {2},
     year = {1990},
     pages = {227-271},
     zbl = {0717.32006},
     mrnumber = {1076253},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1990_4_17_2_227_0}
}
Tworzewski, Piotr. Intersections of analytic sets with linear subspaces. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 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 758691 | Zbl 0558.32002

[2] S. Bochner - W.T. Martin, Several complex variables, Princeton, 1948. | MR 27863 | Zbl 0041.05205

[3] C. Chevalley, Introduction to the theory of algebraic functions of one variable, AMS, New York, 1951. | MR 42164 | Zbl 0045.32301

[4] J. Dieudonné, Fundations of modern analysis, New York, 1960. | MR 120319 | Zbl 0100.04201

[5] E. Fortuna - S. Lojasiewicz, Sur L'algébricité des ensembles analytiques complexes, J. reine angew. Math., 329 (1981), pp. 215-220. | MR 636455 | Zbl 0463.32009

[6] E. Fortuna - S. Lojasiewicz - M. Raimondo, Algébricité de germes analytiques, Dipartimento di Matematica, Università di Pisa, 142 (1986), pp. 1-14. | MR 876225

[7] P. Griffiths - J. Harris, Principles of Algebraic Geometry, Harvard University, 1978. | MR 507725

[8] L. Gruman, The are of analytic varieties in Cn, Math. Scand., 41 (1977), pp. 365-397. | MR 477126 | Zbl 0376.32008

[9] L. Gruman, La géométrie globale des ensembles analytiques dans Cn, Seminaire P. Lelong, H. Skoda 1978-79, pp. 90-99. | MR 599020 | Zbl 0446.32007

[10] R.C. Gunning - H. Rossi, Analytic functions of several complex variables, Englewood Cliffs, N.J., 1965. | MR 180696 | Zbl 0141.08601

[11] M. Herve, Several complex variables, local theory, Oxford University Press, Bombay, 1963. | Zbl 0113.29003

[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 0583.32045

[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 0537.32009

[18] D. Mumford, Algebraic Geometry I, Springer Verlag, 1976. | Zbl 0356.14002

[19] W. Rudin, A geometric criterion for algebraic varieties, J. Math. Mech., 17, 7 (1968), pp. 671-683. | Zbl 0157.13202

[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 0477.32031

[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 82175 | Zbl 0075.30401

[23] N. Sibony - P.M. Wong, Some results on global analytic sets, Seminaire P. Lelong, H. Skoda, 1978-79, pp. 221-237. | MR 599029 | Zbl 0444.32006

[24] J. Siciak, A note on rational functions of several complex variables, Ann. Polon. Math., 12 (1962), pp. 139-142. | MR 147669 | Zbl 0108.07803

[25] J. Siciak, Extremal Plurisubharmonic Functions and Capacities in Cn, Sophia University, Tokyo, 1982. | Zbl 0579.32025

[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 166393 | Zbl 0126.09502

[27] W. Stoll, Invariant forms on Grassmann manifolds, Princeton, 1977. | MR 481089 | Zbl 0398.32016

[28] P. Tworzewski, Some conditions for the algebraicity of analytic sets, Bull. Ac. Pol. Math. XXIX, 11-12 (1981), pp. 545-548. | MR 654212 | Zbl 0508.32009

[29] P. Tworzewski - T. Winiarski, Analytic sets with proper projections, J. reine angew. Math., 337 (1982), pp. 68-76. | MR 676042 | Zbl 0497.32024

[30] P. Tworzewski - T. Winiarski, Limits of algebraic sets of bounded degree, Univ. lagellonicae Acta Math., XXIV (1984), pp. 151-153. | MR 815897 | Zbl 0551.32008

[31] H. Whitney, Complex Analytic Varieties, Princeton, 1972. | MR 387634

[32] T. Winiarski, Continuity of total number of intersection, Ann. Polon. Math. XLVII (1986), pp. 155-178. | MR 884933 | Zbl 0638.32011