Polar classes of singular varieties
Piene, Ragni
Annales scientifiques de l'École Normale Supérieure, Tome 11 (1978), p. 247-276 / Harvested from Numdam
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@article{ASENS_1978_4_11_2_247_0,
     author = {Piene, Ragni},
     title = {Polar classes of singular varieties},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {11},
     year = {1978},
     pages = {247-276},
     doi = {10.24033/asens.1346},
     mrnumber = {80j:14051},
     zbl = {0401.14007},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_1978_4_11_2_247_0}
}

Piene, Ragni. Polar classes of singular varieties. Annales scientifiques de l'École Normale Supérieure, Tome 11 (1978) pp. 247-276. doi : 10.24033/asens.1346. http://gdmltest.u-ga.fr/item/ASENS_1978_4_11_2_247_0/

[A-K] A. Altman and S. L. Kleiman, Introduction to Grothendieck Duality Theory (Lecture Notes in Math., No. 146, Springer-Verlag, 1970). | MR 43 #224 | Zbl 0215.37201

[Ba] H. F. Baker, Principles of Geometry, Vol. VI, Introduction to the Theory of Algebraic Surfaces and Higher Loci, Cambridge Univ. Press, 1933. | Zbl 0008.21907

[Be] L. Berzolari, Allgemeine Theorie der höheren ebenen algebraischen Kurven (Enzyklopädie der Math. Wissenschaften, Vol. III, C. 4. Leipzig, 1906). | JFM 37.0594.04

[E] M. Eger, Sur les systèmes canoniques d'une variété algébrique (C. R. Acad. Sc., Paris, T. 204. 1937, pp. 217-219). | JFM 63.0626.03 | Zbl 0015.27201

[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). | Numdam

[E-C] F. Enriques et O. Chisini, Teoria Geometrica delle Equazioni, Vol. II, Bologna, 1918.

[Fi] H. Fitting, Die Determinentalideale eines Moduls (Jber. Deutsch. Math.-Verein, Vol. 46, 1936, pp. 195-228). | JFM 62.1104.02 | Zbl 0016.05003

[Fu] W. Fulton, Rational Equivalence on Singular Varieties (Publ. Math. I.H.E.S., Vol. 45, Paris, 1976). | Numdam | Zbl 0332.14002

[F-M] W. Fulton and R. Macpherson (to appear).

[G-R] L. Gruson et M. Raynaud, Critères de platitude et de projectivité (Inv. Math., Vol. 13, 1971, pp. 1-89). | MR 46 #7219 | Zbl 0227.14010

[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). | MR 19,881b | Zbl 0099.15702

[Ho] M. Hochster, Grassmannians and their Schubert Subvarieties are Arithmetically Cohen-Macaulay (J. Algebra, Vol. 25, 1973, pp. 40-57). | MR 47 #3383 | Zbl 0256.14024

[Ka] I. Kaplansky, Commutative rings, The Univ. of Chicago Press, 1974 (rev. ed.). | MR 49 #10674 | Zbl 0296.13001

[K-L] G. Kempf and D. Laksov, The Determinantal Formula of Schubert calculus (Acta Math., Vol. 132, 1974, pp. 153-162). | MR 49 #2773 | Zbl 0295.14023

[Kl 1] S. L. Kleiman, The Transversality of a General Translate (Comp. Math., Vol. 38, 1974, pp. 287-297). | Numdam | MR 50 #13063 | Zbl 0288.14014

[Kl 2] S. L. Kleiman, The Enumerative Theory of Singularities (in Real and Complex Singularities, Oslo 1976 (Sijthoff and Noordhoff)). | Zbl 0385.14018

[Lk] D. Laksov, The Arithmetic Cohen-Macaulay Character of Schubert Schemes (Acta Math., Vol. 129, 1972, pp. 1-9). | Zbl 0233.14012

[Lx] A. Lascoux, Puissances extérieures, déterminants et cycles de Schubert (Bull. Soc. math. Fr., T. 102, 1974, pp. 161-179). | Numdam | MR 51 #529 | Zbl 0295.14024

[Lm] G. Laumon, Degré de la variété duale d'une hypersurface à singularités isolées (Bull. Soc. math. Fr., T. 104, 1976, pp. 51-63). | Numdam | MR 54 #2650 | Zbl 0343.14014

[Ll] E. Lluis, De las singularidades que aparacen al proyectar variedades algebraicas (Bol. Soc. Mat. Mexicana, Ser. 2, Vol. 1, 1956, pp. 1-9). | Zbl 0072.16102

[N] A. Nobile, Some Properties of the Nash blowing-up (Pac. J. Math., Vol. 60, 1975, pp. 297-305). | MR 53 #13217 | Zbl 0324.32012

[Pi] R. Piene, Numerical characters of a Curve in Projective n-space in Real and Complex Singularities, Oslo 1976 (Sijthoff and Noordhoff)). | Zbl 0375.14017

[Pl] J. Plücker, Theorie der algebraischen Kurven, Bonn, 1839.

[Ph 1] W. F. Pohl, Differential Geometry of Higher Order (Topology, Vol. 1, 1962, pp. 169-211). | MR 27 #4242 | Zbl 0112.36605

[Ph 2] W. F. Pohl, Extrinsic Complex Projective Geometry (Proc. Conf. Complex Analysis, Minneapolis, Springer-Verlag, Berlin, 1965). | MR 30 #5335 | Zbl 0144.44401

[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.

[Pt] I. R. Porteous, Todd's Canonical Classes, Liverpool singularities symposium I (Lecture Notes in Math., No. 192, Springer-Verlag, 1971). | Zbl 0227.57011

[Rb 1] J. Roberts, Generic Projections of Algebraic Varieties (Amer. J. Math., Vol. 93, 1971, pp. 191-215). | MR 43 #3263 | Zbl 0212.53801

[Rb 2] J. Roberts, A Stratification of the Dual Variety (Summary of results with indications of proof), Preprint, 1976.

[Rs] M. Rosenlicht, Equivalence Relation on Algebraic curves (Ann. of Math., Vol. 56, 1952, pp. 169-191). | MR 14,80c | Zbl 0047.14503

[Rt] L. Roth, Some Formulas for Primals in Four Dimensions (Proc. London Math. Soc., Ser. 2, Vol. 35, 1933, pp. 540-550). | JFM 59.0652.01 | Zbl 0007.22601

[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). | MR 50 #7134 | Zbl 0246.14001

[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). | MR 50 #7135 | Zbl 0284.14006

[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). | JFM 34.0699.01

[Te] B. Teissier, Sur diverses conditions numériques d'équisingularité des familles de courbes, preprint, 1975.

[To] J. A. Todd, The Arithmetical Invariants of Algebraic loci (Proc. London Math. Soc., Vol. 43, 1937, pp. 190-225). | JFM 63.0624.03 | Zbl 0017.18504

[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). | Numdam | Zbl 0349.14001

[Wk] R. J. Walker, Algebraic Curves, Dover Publ., New York, 1962. | MR 26 #2438 | Zbl 0103.38202

[Wl] W. Wallace, Tangency and Duality over Arbitrary Fields (Proc. London Math. Soc., (3), Vol. 6, 1956, pp. 321-342). | MR 18,234b | Zbl 0072.16002