×

Polar classes of singular varieties. (English) Zbl 0401.14007


MSC:

14N10 Enumerative problems (combinatorial problems) in algebraic geometry
14N05 Projective techniques in algebraic geometry
14M10 Complete intersections
14E15 Global theory and resolution of singularities (algebro-geometric aspects)
14C99 Cycles and subschemes
PDF BibTeX XML Cite
Full Text: DOI Numdam EuDML

References:

[1] 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 · Zbl 0215.37201
[2] 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 · Zbl 0008.21907
[3] L. BERZOLARI , Allgemeine Theorie der höheren ebenen algebraischen Kurven (Enzyklopädie der Math. Wissenschaften, Vol. III, C. 4. Leipzig, 1906 ). JFM 37.0594.04 · JFM 37.0594.04
[4] M. EGER , Sur les systèmes canoniques d’une variété algébrique (C. R. Acad. Sc., Paris, T. 204. 1937 , pp. 217-219). Zbl 0015.27201 | JFM 63.0626.03 · Zbl 0015.27201
[5] 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 · Zbl 0203.23301
[6] F. ENRIQUES et O. CHISINI , Teoria Geometrica delle Equazioni , Vol. II, Bologna, 1918 . · JFM 60.1058.03
[7] H. FITTING , Die Determinentalideale eines Moduls (Jber. Deutsch. Math.-Verein, Vol. 46, 1936 , pp. 195-228). Article | Zbl 0016.05003 | JFM 62.1104.02 · Zbl 0016.05003
[8] W. FULTON , Rational Equivalence on Singular Varieties (Publ. Math. I.H.E.S., Vol. 45, Paris, 1976 ). Numdam | Zbl 0332.14002 · Zbl 0332.14002
[9] W. FULTON and R. MACPHERSON (to appear).
[10] 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 · Zbl 0227.14010
[11] 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). Article | MR 19,881b | Zbl 0099.15702 · Zbl 0099.15702
[12] 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 · Zbl 0256.14024
[13] I. KAPLANSKY , Commutative rings , The Univ. of Chicago Press, 1974 (rev. ed.). MR 49 #10674 | Zbl 0296.13001 · Zbl 0296.13001
[14] 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 · Zbl 0295.14023
[15] S. L. KLEIMAN , The Transversality of a General Translate (Comp. Math., Vol. 38, 1974 , pp. 287-297). Numdam | MR 50 #13063 | Zbl 0288.14014 · Zbl 0288.14014
[16] S. L. KLEIMAN , The Enumerative Theory of Singularities (in Real and Complex Singularities, Oslo 1976 (Sijthoff and Noordhoff)). Zbl 0385.14018 · Zbl 0385.14018
[17] D. LAKSOV , The Arithmetic Cohen-Macaulay Character of Schubert Schemes (Acta Math., Vol. 129, 1972 , pp. 1-9). Zbl 0233.14012 · Zbl 0233.14012
[18] 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 · Zbl 0295.14024
[19] 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 · Zbl 0343.14014
[20] 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 · Zbl 0072.16102
[21] A. NOBILE , Some Properties of the Nash blowing-up (Pac. J. Math., Vol. 60, 1975 , pp. 297-305). Article | MR 53 #13217 | Zbl 0324.32012 · Zbl 0324.32012
[22] R. PIENE , Numerical characters of a Curve in Projective n-space in Real and Complex Singularities, Oslo 1976 (Sijthoff and Noordhoff)). Zbl 0375.14017 · Zbl 0375.14017
[23] J. PLÜCKER , Theorie der algebraischen Kurven , Bonn, 1839 .
[24] W. F. POHL , Differential Geometry of Higher Order (Topology, Vol. 1, 1962 , pp. 169-211). MR 27 #4242 | Zbl 0112.36605 · Zbl 0112.36605
[25] W. F. POHL , Extrinsic Complex Projective Geometry (Proc. Conf. Complex Analysis, Minneapolis, Springer-Verlag, Berlin, 1965 ). MR 30 #5335 | Zbl 0144.44401 · Zbl 0144.44401
[26] 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] I. R. PORTEOUS , Todd’s Canonical Classes, Liverpool singularities symposium I (Lecture Notes in Math., No. 192, Springer-Verlag, 1971 ). Zbl 0227.57011 · Zbl 0227.57011
[28] J. ROBERTS , Generic Projections of Algebraic Varieties (Amer. J. Math., Vol. 93, 1971 , pp. 191-215). MR 43 #3263 | Zbl 0212.53801 · Zbl 0212.53801
[29] J. ROBERTS , A Stratification of the Dual Variety (Summary of results with indications of proof), Preprint, 1976 .
[30] M. ROSENLICHT , Equivalence Relation on Algebraic curves (Ann. of Math., Vol. 56, 1952 , pp. 169-191). MR 14,80c | Zbl 0047.14503 · Zbl 0047.14503
[31] L. ROTH , Some Formulas for Primals in Four Dimensions (Proc. London Math. Soc., Ser. 2, Vol. 35, 1933 , pp. 540-550). Zbl 0007.22601 | JFM 59.0652.01 · Zbl 0007.22601
[32] 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 · Zbl 0246.14001
[33] 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 · Zbl 0284.14006
[34] 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 · JFM 34.0699.01
[35] B. TEISSIER , Sur diverses conditions numériques d’équisingularité des familles de courbes , preprint, 1975 .
[36] J. A. TODD , The Arithmetical Invariants of Algebraic loci (Proc. London Math. Soc., Vol. 43, 1937 , pp. 190-225). Zbl 0017.18504 | JFM 63.0624.03 · Zbl 0017.18504
[37] 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 · Zbl 0349.14001
[38] R. J. WALKER , Algebraic Curves , Dover Publ., New York, 1962 . MR 26 #2438 | Zbl 0103.38202 · Zbl 0103.38202
[39] 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 · Zbl 0072.16002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.