# 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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topFriedman, 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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- [FM] R. Friedman and R. Miranda: Smoothing cusp singularities of small length, to appear in Math. Annalen. Zbl0488.14006
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- [La2] H. Laufer: On minimally elliptic singularities. Am. J. Math.99 (1977) 1257-1295. Zbl0384.32003MR568898
- [La3] H. Laufer: Simultaneous resolution of some families of isolated surface singularities, to appear in the Arcata singularities volume.
- [L1] E. Looijenga: Rational surfaces with an effective anticanonical divisor. Annals of Math114 (1981) 267-322. Zbl0509.14035MR632841
- [L2] E. Looijenga: The smoothing components of a triangle singularity, to appear in the Arcata singularities volume. Zbl0568.14002
- [N] V.V. Nikulin: Integral symmetric bilinear forms and some of their applications. Math. USSR Izvestiya14 (1980) 103-167. Zbl0427.10014
- [P0] H. Pinkham: Deformations of algebraic varieties with G m action. Asterisque20 (1974) Soc. Math. France. Zbl0304.14006MR376672
- [P1] H. Pinkham: Groupe de monodromie des singularités unimodulaires exceptionnelles, C.R. Acad. Sc. Paris284 (A) (20 Juin 1977) 1515-1518. Zbl0391.14005MR439840
- [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.
- [P3] H. Pinkham: Automorphisms of cusps and Inoue-Hirzebruch surfaces. Comp. Math.52 (1984) 299-313. Zbl0573.14015MR756724
- [P4] H. Pinkham: Deformations of normal surface singularities with C* action. Math. Ann.232 (1978) 65-84. Zbl0351.14004MR498543
- [S] J.-P. Serre: Cours d'arithmétique. Paris, P.U.F. (1970). Zbl0225.12002
- [W1] J. Wahl: Elliptic deformations of minimally elliptic singularities. Math. Ann.253 (1980) 241-262. Zbl0431.14012MR597833
- [W2] J. Wahl: Smoothings of normal surface singularities. Topology20 (1981) 219-246. Zbl0484.14012MR608599
- [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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