@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}, pages = {247--276}, publisher = {Elsevier}, volume = {Ser. 4, 11}, number = {2}, year = {1978}, doi = {10.24033/asens.1346}, mrnumber = {80j:14051}, zbl = {0401.14007}, language = {en}, url = {http://archive.numdam.org/articles/10.24033/asens.1346/} }
TY - JOUR AU - Piene, Ragni TI - Polar classes of singular varieties JO - Annales scientifiques de l'École Normale Supérieure PY - 1978 SP - 247 EP - 276 VL - 11 IS - 2 PB - Elsevier UR - http://archive.numdam.org/articles/10.24033/asens.1346/ DO - 10.24033/asens.1346 LA - en ID - ASENS_1978_4_11_2_247_0 ER -
Piene, Ragni. Polar classes of singular varieties. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 11 (1978) no. 2, pp. 247-276. doi : 10.24033/asens.1346. http://archive.numdam.org/articles/10.24033/asens.1346/
[A-K] Introduction to Grothendieck Duality Theory (Lecture Notes in Math., No. 146, Springer-Verlag, 1970). | MR | Zbl
and ,[Ba] Principles of Geometry, Vol. VI, Introduction to the Theory of Algebraic Surfaces and Higher Loci, Cambridge Univ. Press, 1933. | Zbl
,[Be] Allgemeine Theorie der höheren ebenen algebraischen Kurven (Enzyklopädie der Math. Wissenschaften, Vol. III, C. 4. Leipzig, 1906). | JFM
,[E] Sur les systèmes canoniques d'une variété algébrique (C. R. Acad. Sc., Paris, T. 204. 1937, pp. 217-219). | JFM | Zbl
,[EGA IV] Éléments de géométrie algébrique, IV (Publ. Math. I.H.E.S., Vol. 20, 24, 28, 32, Paris, 1964-1967). | Numdam
et ,[E-C] Teoria Geometrica delle Equazioni, Vol. II, Bologna, 1918.
et ,[Fi] Die Determinentalideale eines Moduls (Jber. Deutsch. Math.-Verein, Vol. 46, 1936, pp. 195-228). | JFM | Zbl
,[Fu] Rational Equivalence on Singular Varieties (Publ. Math. I.H.E.S., Vol. 45, Paris, 1976). | Numdam | Zbl
,[F-M]
and (to appear).[G-R] Critères de platitude et de projectivité (Inv. Math., Vol. 13, 1971, pp. 1-89). | MR | Zbl
et ,[Hi] 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 | Zbl
,[Ho] Grassmannians and their Schubert Subvarieties are Arithmetically Cohen-Macaulay (J. Algebra, Vol. 25, 1973, pp. 40-57). | MR | Zbl
,[Ka] Commutative rings, The Univ. of Chicago Press, 1974 (rev. ed.). | MR | Zbl
,[K-L] The Determinantal Formula of Schubert calculus (Acta Math., Vol. 132, 1974, pp. 153-162). | MR | Zbl
and ,[Kl 1] The Transversality of a General Translate (Comp. Math., Vol. 38, 1974, pp. 287-297). | Numdam | MR | Zbl
,[Kl 2] The Enumerative Theory of Singularities (in Real and Complex Singularities, Oslo 1976 (Sijthoff and Noordhoff)). | Zbl
,[Lk] The Arithmetic Cohen-Macaulay Character of Schubert Schemes (Acta Math., Vol. 129, 1972, pp. 1-9). | Zbl
,[Lx] Puissances extérieures, déterminants et cycles de Schubert (Bull. Soc. math. Fr., T. 102, 1974, pp. 161-179). | Numdam | MR | Zbl
,[Lm] Degré de la variété duale d'une hypersurface à singularités isolées (Bull. Soc. math. Fr., T. 104, 1976, pp. 51-63). | Numdam | MR | Zbl
,[Ll] De las singularidades que aparacen al proyectar variedades algebraicas (Bol. Soc. Mat. Mexicana, Ser. 2, Vol. 1, 1956, pp. 1-9). | Zbl
,[N] Some Properties of the Nash blowing-up (Pac. J. Math., Vol. 60, 1975, pp. 297-305). | MR | Zbl
,[Pi] Numerical characters of a Curve in Projective n-space in Real and Complex Singularities, Oslo 1976 (Sijthoff and Noordhoff)). | Zbl
,[Pl] Theorie der algebraischen Kurven, Bonn, 1839.
,[Ph 1] Differential Geometry of Higher Order (Topology, Vol. 1, 1962, pp. 169-211). | MR | Zbl
,[Ph 2] Extrinsic Complex Projective Geometry (Proc. Conf. Complex Analysis, Minneapolis, Springer-Verlag, Berlin, 1965). | MR | Zbl
,[Po] 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] Todd's Canonical Classes, Liverpool singularities symposium I (Lecture Notes in Math., No. 192, Springer-Verlag, 1971). | Zbl
,[Rb 1] Generic Projections of Algebraic Varieties (Amer. J. Math., Vol. 93, 1971, pp. 191-215). | MR | Zbl
,[Rb 2] A Stratification of the Dual Variety (Summary of results with indications of proof), Preprint, 1976.
,[Rs] Equivalence Relation on Algebraic curves (Ann. of Math., Vol. 56, 1952, pp. 169-191). | MR | Zbl
,[Rt] Some Formulas for Primals in Four Dimensions (Proc. London Math. Soc., Ser. 2, Vol. 35, 1933, pp. 540-550). | JFM | Zbl
,[SGA 7 I] Formal Deformation Theory, Exposé VI in Groupes de Monodromie en Géométrie algébrique (SGA 7) (Lecture Notes in Math., No. 288, Springer-Verlag, 1972). | MR | Zbl
,[SGA 7 II] Pinceaux de Lefschetz : théorème d'existence, Exp. XVII in Groupes de Monodrome... (SGA 7) (Lecture Notes in Math., No. 340, Springer-Verlag, 1973). | MR | Zbl
,[S] 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
,[Te] Sur diverses conditions numériques d'équisingularité des familles de courbes, preprint, 1975.
,[To] The Arithmetical Invariants of Algebraic loci (Proc. London Math. Soc., Vol. 43, 1937, pp. 190-225). | JFM | Zbl
,[V] 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
,[Wk] Algebraic Curves, Dover Publ., New York, 1962. | MR | Zbl
,[Wl] Tangency and Duality over Arbitrary Fields (Proc. London Math. Soc., (3), Vol. 6, 1956, pp. 321-342). | MR | Zbl
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