Intersections of analytic sets with linear subspaces

Piotr Tworzewski

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1990)

  • Volume: 17, Issue: 2, page 227-271
  • ISSN: 0391-173X

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Tworzewski, Piotr. "Intersections of analytic sets with linear subspaces." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 17.2 (1990): 227-271. <http://eudml.org/doc/84072>.

@article{Tworzewski1990,
author = {Tworzewski, Piotr},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {algebraic sets; Nash germs; intersections of germs of analytic sets},
language = {eng},
number = {2},
pages = {227-271},
publisher = {Scuola normale superiore},
title = {Intersections of analytic sets with linear subspaces},
url = {http://eudml.org/doc/84072},
volume = {17},
year = {1990},
}

TY - JOUR
AU - Tworzewski, Piotr
TI - Intersections of analytic sets with linear subspaces
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1990
PB - Scuola normale superiore
VL - 17
IS - 2
SP - 227
EP - 271
LA - eng
KW - algebraic sets; Nash germs; intersections of germs of analytic sets
UR - http://eudml.org/doc/84072
ER -

References

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  1. [1] J. Bochnak - W. Kucharz, Local algebraicity of analytic sets, J. reine angew. Math., 352 (1984), pp. 1-14. Zbl0558.32002MR758691
  2. [2] S. Bochner - W.T. Martin, Several complex variables, Princeton, 1948. Zbl0041.05205MR27863
  3. [3] C. Chevalley, Introduction to the theory of algebraic functions of one variable, AMS, New York, 1951. Zbl0045.32301MR42164
  4. [4] J. Dieudonné, Fundations of modern analysis, New York, 1960. Zbl0100.04201MR120319
  5. [5] E. Fortuna - S. Lojasiewicz, Sur L'algébricité des ensembles analytiques complexes, J. reine angew. Math., 329 (1981), pp. 215-220. Zbl0463.32009MR636455
  6. [6] E. Fortuna - S. Lojasiewicz - M. Raimondo, Algébricité de germes analytiques, Dipartimento di Matematica, Università di Pisa, 142 (1986), pp. 1-14. Zbl0599.32004MR876225
  7. [7] P. Griffiths - J. Harris, Principles of Algebraic Geometry, Harvard University, 1978. MR507725
  8. [8] L. Gruman, The are of analytic varieties in Cn, Math. Scand., 41 (1977), pp. 365-397. Zbl0376.32008MR477126
  9. [9] L. Gruman, La géométrie globale des ensembles analytiques dans Cn, Seminaire P. Lelong, H. Skoda 1978-79, pp. 90-99. Zbl0446.32007MR599020
  10. [10] R.C. Gunning - H. Rossi, Analytic functions of several complex variables, Englewood Cliffs, N.J., 1965. Zbl0141.08601MR180696
  11. [11] M. Herve, Several complex variables, local theory, Oxford University Press, Bombay, 1963. Zbl0113.29003
  12. [12] M. Jarnicki - P. Tworzewski, A note on holomorphic functions with polynomial growth, Osnabrücker Shriften zur Mathematik, 67 (1983), pp. 1-12. 
  13. [13] M. Koronevskij, Kriterij ratsional'nosti i psevdoratsional'nosti funktsij, Teorija funktsij i funktsional'nyj analiz, Prilozhenija, 18 (1973), pp. 91-102. 
  14. [14] F. Leja, Teoria funckji analitycznych, Warszawa, 1957. 
  15. [15] S. Lojasiewicz, Ensembles semi-analytiques, I.H.E.S., Bures-sur-Yvette, 1965. 
  16. [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. Zbl0583.32045
  17. [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. Zbl0537.32009
  18. [18] D. Mumford, Algebraic Geometry I, Springer Verlag, 1976. Zbl0356.14002
  19. [19] W. Rudin, A geometric criterion for algebraic varieties, J. Math. Mech., 17, 7 (1968), pp. 671-683. Zbl0157.13202
  20. [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. Zbl0477.32031
  21. [21] A. Sadullaev, Kriterij algebraichnosti analiticheskikh mnozhestv, Sbornik o golomorfnykh funktsijakh mnogikh kompleksnykh peremennykh, Krasnojarsk, 1976, pp. 107-122. 
  22. [22] J.P. Serre, Géométrie algébrique et géométrie analytique, Ann. Inst. Fourier, GrenobleVI (1955-56), pp. 1-42. Zbl0075.30401MR82175
  23. [23] N. Sibony - P.M. Wong, Some results on global analytic sets, Seminaire P. Lelong, H. Skoda, 1978-79, pp. 221-237. Zbl0444.32006MR599029
  24. [24] J. Siciak, A note on rational functions of several complex variables, Ann. Polon. Math., 12 (1962), pp. 139-142. Zbl0108.07803MR147669
  25. [25] J. Siciak, Extremal Plurisubharmonic Functions and Capacities in Cn, Sophia University, Tokyo, 1982. Zbl0579.32025
  26. [26] W. Stoll, The growth of the area of a transcendental analytic set I, II, Math. Ann., 156 (1964), pp. 47-78, 144-170. Zbl0126.09502MR166393
  27. [27] W. Stoll, Invariant forms on Grassmann manifolds, Princeton, 1977. Zbl0398.32016MR481089
  28. [28] P. Tworzewski, Some conditions for the algebraicity of analytic sets, Bull. Ac. Pol. Math.XXIX, 11-12 (1981), pp. 545-548. Zbl0508.32009MR654212
  29. [29] P. Tworzewski - T. Winiarski, Analytic sets with proper projections, J. reine angew. Math., 337 (1982), pp. 68-76. Zbl0497.32024MR676042
  30. [30] P. Tworzewski - T. Winiarski, Limits of algebraic sets of bounded degree, Univ. lagellonicae Acta Math., XXIV (1984), pp. 151-153. Zbl0551.32008MR815897
  31. [31] H. Whitney, Complex Analytic Varieties, Princeton, 1972. Zbl0265.32008MR387634
  32. [32] T. Winiarski, Continuity of total number of intersection, Ann. Polon. Math.XLVII (1986), pp. 155-178. Zbl0638.32011MR884933

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