Smoothings of cusp singularities via triangle singularities

Robert Friedman; Henry Pinkham

Compositio Mathematica (1984)

  • Volume: 53, Issue: 3, page 303-316
  • ISSN: 0010-437X

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Friedman, Robert, and Pinkham, Henry. "Smoothings of cusp singularities via triangle singularities." Compositio Mathematica 53.3 (1984): 303-316. <http://eudml.org/doc/89689>.

@article{Friedman1984,
author = {Friedman, Robert, Pinkham, Henry},
journal = {Compositio Mathematica},
keywords = {minimal resolution of the dual of a smoothable two dimensional; cusp singularity; anticanonical divisor on a rational surface; smoothability; versal deformation of the triangle singularity; minimal resolution of the dual of a smoothable two dimensional cusp singularity},
language = {eng},
number = {3},
pages = {303-316},
publisher = {Martinus Nijhoff Publishers},
title = {Smoothings of cusp singularities via triangle singularities},
url = {http://eudml.org/doc/89689},
volume = {53},
year = {1984},
}

TY - JOUR
AU - Friedman, Robert
AU - Pinkham, Henry
TI - Smoothings of cusp singularities via triangle singularities
JO - Compositio Mathematica
PY - 1984
PB - Martinus Nijhoff Publishers
VL - 53
IS - 3
SP - 303
EP - 316
LA - eng
KW - minimal resolution of the dual of a smoothable two dimensional; cusp singularity; anticanonical divisor on a rational surface; smoothability; versal deformation of the triangle singularity; minimal resolution of the dual of a smoothable two dimensional cusp singularity
UR - http://eudml.org/doc/89689
ER -

References

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  1. [F] R. Friedman: Global smoothings of varieties with normal crossings, to appear in Annals of Math. Zbl0569.14002
  2. [FM] R. Friedman and R. Miranda: Smoothing cusp singularities of small length, to appear in Math. Annalen. Zbl0488.14006
  3. [La1] H. Laufer: Taut two dimensional singularities. Math. Ann.205 (1973) 131-164. Zbl0281.32010MR333238
  4. [La2] H. Laufer: On minimally elliptic singularities. Am. J. Math.99 (1977) 1257-1295. Zbl0384.32003MR568898
  5. [La3] H. Laufer: Simultaneous resolution of some families of isolated surface singularities, to appear in the Arcata singularities volume. 
  6. [L1] E. Looijenga: Rational surfaces with an effective anticanonical divisor. Annals of Math114 (1981) 267-322. Zbl0509.14035MR632841
  7. [L2] E. Looijenga: The smoothing components of a triangle singularity, to appear in the Arcata singularities volume. Zbl0568.14002
  8. [N] V.V. Nikulin: Integral symmetric bilinear forms and some of their applications. Math. USSR Izvestiya14 (1980) 103-167. Zbl0427.10014
  9. [P0] H. Pinkham: Deformations of algebraic varieties with G m action. Asterisque20 (1974) Soc. Math. France. Zbl0304.14006MR376672
  10. [P1] H. Pinkham: Groupe de monodromie des singularités unimodulaires exceptionnelles, C.R. Acad. Sc. Paris284 (A) (20 Juin 1977) 1515-1518. Zbl0391.14005MR439840
  11. [P2] H. Pinkham: Smoothings of the Dp,q,r singularities, p + q + r = 22. Appendix to a paper of E. LOOIJENGA, to appear in the Arcata singularities volume. 
  12. [P3] H. Pinkham: Automorphisms of cusps and Inoue-Hirzebruch surfaces. Comp. Math.52 (1984) 299-313. Zbl0573.14015MR756724
  13. [P4] H. Pinkham: Deformations of normal surface singularities with C* action. Math. Ann.232 (1978) 65-84. Zbl0351.14004MR498543
  14. [S] J.-P. Serre: Cours d'arithmétique. Paris, P.U.F. (1970). Zbl0225.12002
  15. [W1] J. Wahl: Elliptic deformations of minimally elliptic singularities. Math. Ann.253 (1980) 241-262. Zbl0431.14012MR597833
  16. [W2] J. Wahl: Smoothings of normal surface singularities. Topology20 (1981) 219-246. Zbl0484.14012MR608599
  17. [W3] J. Wahl: Derivations of negative weight and non-smoothability of certain singularities. Math. Ann.258 (1982) 383-398. Zbl0507.14029MR650944

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