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Original Articles

Existence of Hypersurfaces with Prescribed Simple Singularities

Pages 335-356 | Received 19 Sep 2001, Published online: 01 Feb 2007

References

  • Bruce , J. W. 1981 . An upper bound for the number of singularities on a projective hypersurface . Bull. Lond. Math. Soc. , 13 : 47 – 50 .
  • Chmutov , S. V. 1992 . Examples of projective surfaces with many singularities . J. Algebraic Geom. , 1 ( 2 ) : 191 – 196 .
  • du Plessis , A. A. and Wall , C. T. C. 1998 . Versal deformations in spaces of polynomials of fixed weight . Compositio Math. , 114 ( 2 ) : 113 – 124 .
  • Endrass , S. 1997 . A projective surface of degree eight with 168 nodes . J. Algebraic Geom. , 6 ( 2 ) : 325 – 334 .
  • Endrass S., Persson U., Stevens J. (2000). Surfaces with triple points, Preprint math.AG/0010163
  • Greuel , G.-M. and Karras , U. 1989 . Families of varieties with prescribed singularities . Compositio Math. , 69 ( 1 ) : 83 – 110 .
  • Greuel , G.-M. and Lossen , C. 1996 . Equianalytic and equisingular families of curves on a surfaces . Manuscr. Math. , 91 : 323 – 342 .
  • Greuel , G.-M. , Lossen , C. and Shustin , E. 1998 . Plane curves of minimal degree with prescribed singularities . Invent. Math. , 133 : 539 – 580 .
  • Hirano , A. 1992 . Constructions of plane curves with cusps . Saitama Math. J. , 10 : 21 – 24 .
  • Hirschowitz , A. 1985 . Le methode d'Horace pour l'interpolation à plusieurs variables . Manusc. Math. , 50 : 337 – 388 .
  • Itenberg , I. and Shustin , E. 1996 . Real algebraic curves with real cusps . Amer. Math. Soc. Transl. , 173 ( 2 ) : 97 – 109 .
  • Ivinskis, K. Normale Flächen und die Miyaoka-Kobayashi-Ungleichung, Diplomarbeit, University of Bonn, 1985
  • Lossen , C. 1999 . New asymptotics for the existence of plane curves with prescribed singularities . Comm. Algebra , 27 : 3263 – 3282 .
  • Miyaoka , Y. 1984 . The maximal number of quotient singularities on surfaces with given numerical invariants . Math. Ann. , 268 : 159 – 171 .
  • Shustin , E. 1997 . Smoothness of equisingular families of plane algebraic curves . Int. Math. Res. Not. , 313 ( 2 ) : 67 – 82 .
  • Shustin , E. 1998 . Gluing of singular and critical points . Topology , 37 ( 1 ) : 195 – 217 .
  • Shustin , E. 2000 . Lower deformations of isolated hypersurface singularities . St. Petersburg Math. J. , 11 ( 5 ) : 883 – 908 .
  • Shustin , E. and Tyomkin , I. 1999 . Versal deformations of algebraic hypersurfaces with isolated singularities . Math. Ann. , 313 ( 2 ) : 297 – 314 .
  • van der Waerden , B. L. 1973 . Einführung in die Algebraische Geometrie , 2nd Berlin-Heidelberg-New York : Springer-Verlag .
  • van Straten , D. 1993 . Aquintic hypersurface in P 4 with 130 nodes . Topology , 32 ( 4 ) : 857 – 864 .
  • Varchenko , A. N. 1983 . On semicontinuity of the spectrum and an upper estimate for the number of singular points of a projective hypersurface. . Sov. Math. Dokl. , 27 : 735 – 739 .
  • Viro , O. Ya. 1984 . “ Gluing of plane real algebraic curves and construction of curves of degrees 6 and 7 ” . In Lect. Notes Math. Vol. 1060 , 187 – 200 . Berlin : Springer .
  • Wahl , J. 1994 . Miyaoka-Yau inequality for normal surfaces and local analogues . Contemp. Math. , 162 : 381 – 402 .

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