Polar classes of singular varieties

Ragni Piene

Annales scientifiques de l'École Normale Supérieure (1978)

  • Volume: 11, Issue: 2, page 247-276
  • ISSN: 0012-9593

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Piene, Ragni. "Polar classes of singular varieties." Annales scientifiques de l'École Normale Supérieure 11.2 (1978): 247-276. <http://eudml.org/doc/82015>.

@article{Piene1978,
author = {Piene, Ragni},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {Polar Locus; Generic Immersions; Chern Classes},
language = {eng},
number = {2},
pages = {247-276},
publisher = {Elsevier},
title = {Polar classes of singular varieties},
url = {http://eudml.org/doc/82015},
volume = {11},
year = {1978},
}

TY - JOUR
AU - Piene, Ragni
TI - Polar classes of singular varieties
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1978
PB - Elsevier
VL - 11
IS - 2
SP - 247
EP - 276
LA - eng
KW - Polar Locus; Generic Immersions; Chern Classes
UR - http://eudml.org/doc/82015
ER -

References

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  1. [A-K] A. ALTMAN and S. L. KLEIMAN, Introduction to Grothendieck Duality Theory (Lecture Notes in Math., No. 146, Springer-Verlag, 1970). Zbl0215.37201MR43 #224
  2. [Ba] H. F. BAKER, Principles of Geometry, Vol. VI, Introduction to the Theory of Algebraic Surfaces and Higher Loci, Cambridge Univ. Press, 1933. Zbl0008.21907
  3. [Be] L. BERZOLARI, Allgemeine Theorie der höheren ebenen algebraischen Kurven (Enzyklopädie der Math. Wissenschaften, Vol. III, C. 4. Leipzig, 1906). JFM37.0594.04
  4. [E] M. EGER, Sur les systèmes canoniques d'une variété algébrique (C. R. Acad. Sc., Paris, T. 204. 1937, pp. 217-219). Zbl0015.27201JFM63.0626.03
  5. [EGA IV] A. GROTHENDIECK et J. DIEUDONNÉ, Éléments de géométrie algébrique, IV (Publ. Math. I.H.E.S., Vol. 20, 24, 28, 32, Paris, 1964-1967). 
  6. [E-C] F. ENRIQUES et O. CHISINI, Teoria Geometrica delle Equazioni, Vol. II, Bologna, 1918. 
  7. [Fi] H. FITTING, Die Determinentalideale eines Moduls (Jber. Deutsch. Math.-Verein, Vol. 46, 1936, pp. 195-228). Zbl0016.05003JFM62.1104.02
  8. [Fu] W. FULTON, Rational Equivalence on Singular Varieties (Publ. Math. I.H.E.S., Vol. 45, Paris, 1976). Zbl0332.14002
  9. [F-M] W. FULTON and R. MACPHERSON (to appear). 
  10. [G-R] L. GRUSON et M. RAYNAUD, Critères de platitude et de projectivité (Inv. Math., Vol. 13, 1971, pp. 1-89). Zbl0227.14010MR46 #7219
  11. [Hi] H. HIRONAKA, On the Arithmetic Genera and the Effective Genera of Algebraic Curves (Mem. Coll. Sc., Univ. Kyoto, Ser. A, Vol. XXX, Math. No. 2, 1956, pp. 177-194). Zbl0099.15702MR19,881b
  12. [Ho] M. HOCHSTER, Grassmannians and their Schubert Subvarieties are Arithmetically Cohen-Macaulay (J. Algebra, Vol. 25, 1973, pp. 40-57). Zbl0256.14024MR47 #3383
  13. [Ka] I. KAPLANSKY, Commutative rings, The Univ. of Chicago Press, 1974 (rev. ed.). Zbl0296.13001MR49 #10674
  14. [K-L] G. KEMPF and D. LAKSOV, The Determinantal Formula of Schubert calculus (Acta Math., Vol. 132, 1974, pp. 153-162). Zbl0295.14023MR49 #2773
  15. [Kl 1] S. L. KLEIMAN, The Transversality of a General Translate (Comp. Math., Vol. 38, 1974, pp. 287-297). Zbl0288.14014MR50 #13063
  16. [Kl 2] S. L. KLEIMAN, The Enumerative Theory of Singularities (in Real and Complex Singularities, Oslo 1976 (Sijthoff and Noordhoff)). Zbl0385.14018
  17. [Lk] D. LAKSOV, The Arithmetic Cohen-Macaulay Character of Schubert Schemes (Acta Math., Vol. 129, 1972, pp. 1-9). Zbl0233.14012
  18. [Lx] A. LASCOUX, Puissances extérieures, déterminants et cycles de Schubert (Bull. Soc. math. Fr., T. 102, 1974, pp. 161-179). Zbl0295.14024MR51 #529
  19. [Lm] G. LAUMON, Degré de la variété duale d'une hypersurface à singularités isolées (Bull. Soc. math. Fr., T. 104, 1976, pp. 51-63). Zbl0343.14014MR54 #2650
  20. [Ll] E. LLUIS, De las singularidades que aparacen al proyectar variedades algebraicas (Bol. Soc. Mat. Mexicana, Ser. 2, Vol. 1, 1956, pp. 1-9). Zbl0072.16102
  21. [N] A. NOBILE, Some Properties of the Nash blowing-up (Pac. J. Math., Vol. 60, 1975, pp. 297-305). Zbl0324.32012MR53 #13217
  22. [Pi] R. PIENE, Numerical characters of a Curve in Projective n-space in Real and Complex Singularities, Oslo 1976 (Sijthoff and Noordhoff)). Zbl0375.14017
  23. [Pl] J. PLÜCKER, Theorie der algebraischen Kurven, Bonn, 1839. 
  24. [Ph 1] W. F. POHL, Differential Geometry of Higher Order (Topology, Vol. 1, 1962, pp. 169-211). Zbl0112.36605MR27 #4242
  25. [Ph 2] W. F. POHL, Extrinsic Complex Projective Geometry (Proc. Conf. Complex Analysis, Minneapolis, Springer-Verlag, Berlin, 1965). Zbl0144.44401MR30 #5335
  26. [Po] J. V. PONCELET, Traité des propriétés projectives des figures, ouvrage utile à ceux qui s'occupent des applications de la géométrie descriptive et d'opérations géométriques sur le terrain, Vol. 2, 2nd éd., Paris, 1865-1866. 
  27. [Pt] I. R. PORTEOUS, Todd's Canonical Classes, Liverpool singularities symposium I (Lecture Notes in Math., No. 192, Springer-Verlag, 1971). Zbl0227.57011
  28. [Rb 1] J. ROBERTS, Generic Projections of Algebraic Varieties (Amer. J. Math., Vol. 93, 1971, pp. 191-215). Zbl0212.53801MR43 #3263
  29. [Rb 2] J. ROBERTS, A Stratification of the Dual Variety (Summary of results with indications of proof), Preprint, 1976. 
  30. [Rs] M. ROSENLICHT, Equivalence Relation on Algebraic curves (Ann. of Math., Vol. 56, 1952, pp. 169-191). Zbl0047.14503MR14,80c
  31. [Rt] L. ROTH, Some Formulas for Primals in Four Dimensions (Proc. London Math. Soc., Ser. 2, Vol. 35, 1933, pp. 540-550). Zbl0007.22601JFM59.0652.01
  32. [SGA 7 I] D. RIM, Formal Deformation Theory, Exposé VI in Groupes de Monodromie en Géométrie algébrique (SGA 7) (Lecture Notes in Math., No. 288, Springer-Verlag, 1972). Zbl0246.14001MR50 #7134
  33. [SGA 7 II] N. KATZ, Pinceaux de Lefschetz : théorème d'existence, Exp. XVII in Groupes de Monodrome... (SGA 7) (Lecture Notes in Math., No. 340, Springer-Verlag, 1973). Zbl0284.14006MR50 #7135
  34. [S] F. SEVERI, Sulle intersezioni delle varietà algebriche e sopra i loro caratteri e singolarità proiettive (Mem. R. Acc. Sc. Torino, S. II, Vol. 52, 1902, pp. 61-118). JFM34.0699.01
  35. [Te] B. TEISSIER, Sur diverses conditions numériques d'équisingularité des familles de courbes, preprint, 1975. 
  36. [To] J. A. TODD, The Arithmetical Invariants of Algebraic loci (Proc. London Math. Soc., Vol. 43, 1937, pp. 190-225). Zbl0017.18504JFM63.0624.03
  37. [V] J.-L. VERDIER, Le théorème de Riemann-Roch pour les variétés algébriques éventuellement singulières (d'après P. BAUM, W. FULTON et R. MACPHERSON) (Séminaire Bourbaki, 27e année, No. 464, 1974-1975). Zbl0349.14001
  38. [Wk] R. J. WALKER, Algebraic Curves, Dover Publ., New York, 1962. Zbl0103.38202MR26 #2438
  39. [Wl] W. WALLACE, Tangency and Duality over Arbitrary Fields (Proc. London Math. Soc., (3), Vol. 6, 1956, pp. 321-342). Zbl0072.16002MR18,234b

Citations in EuDML Documents

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  1. Bernd Bank, Marc Giusti, Joos Heintz, Luis M. Pardo, Generalized polar varieties and an efficient real elimination
  2. Allen Tannenbaum, Families of algebraic curves with nodes
  3. Gerardo Gonzalez-Sprinberg, Désingularisation des surfaces par des modifications de Nash normalisées
  4. Allen Tannenbaum, On the classical characteristic linear series of plane curves with nodes and cuspidal points : two examples of Beniamino Segre
  5. S. Greco, C. Traverso, On seminormal schemes
  6. Michel Merle, Variétés polaires, stratifications de Whitney et classes de Chern des espaces analytiques complexes

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