Automorphisms of cusps and Inoue-Hirzebruch surfaces

H. C. Pinkham

Compositio Mathematica (1984)

  • Volume: 52, Issue: 3, page 299-313
  • ISSN: 0010-437X

How to cite


Pinkham, H. C.. "Automorphisms of cusps and Inoue-Hirzebruch surfaces." Compositio Mathematica 52.3 (1984): 299-313. <>.

author = {Pinkham, H. C.},
journal = {Compositio Mathematica},
keywords = {cusp singularity; automorphism group of an Inoue-Hirzebruch surface},
language = {eng},
number = {3},
pages = {299-313},
publisher = {Martinus Nijhoff Publishers},
title = {Automorphisms of cusps and Inoue-Hirzebruch surfaces},
url = {},
volume = {52},
year = {1984},

AU - Pinkham, H. C.
TI - Automorphisms of cusps and Inoue-Hirzebruch surfaces
JO - Compositio Mathematica
PY - 1984
PB - Martinus Nijhoff Publishers
VL - 52
IS - 3
SP - 299
EP - 313
LA - eng
KW - cusp singularity; automorphism group of an Inoue-Hirzebruch surface
UR -
ER -


  1. [1] V.I. Arnold: Critical points of smooth functions. Proc. Intern. Cong. Math. Vancouver (1974) 19-39. Zbl0343.58002MR431217
  2. [2] A. Ash, D. Mumford, M. Rapoport and Y. Tai: Smooth compactification of locally symmetric varieties. Brookline, Mass: Math. Sci. Press (1975). Zbl0334.14007MR457437
  3. [3] Z.I. Borevich and I.R. Shafarevich: Number Theory. New York: Academic Press (1966). Zbl0145.04902MR195803
  4. [4] R. Friedman and R. Miranda: Smoothing cusp singularities of small length. Math. Annalen263 (1983) 185-212. Zbl0488.14006MR698002
  5. [5] F. Hirzebruch: Hilbert modular surfaces. Enseignement Math.19 (1973) 183-282. Zbl0285.14007MR393045
  6. [6] F. Hirzebruch and D. Zagier: Classification of Hilbert modular surfaces. In: W.L. Baily and T. Shioda (eds.), Complex Analysis and Algebraic Geometry. Cambridge University Press (1977). Zbl0354.14011MR480356
  7. [7] E.L. Ince: Cycles of reduced ideals in quadratic fields. British Assoc. Advancement science, Math. tables, Volume IV, London (1934). Zbl0010.29201JFM62.1156.01
  8. [8] M. Inoue: New surfaces with no meromorphic functions II. In: W.L. Baily and T. Shioda (eds.), Complex Analysis and Algebraic Geometry. Cambridge University Press (1977). Zbl0365.14011
  9. [9] K. Kodaira: On the structure of compact complex analytic surfaces, I and II. Amer. J. Math.86 (1964) 751-798 and 88 (1966) 682-721. Zbl0193.37701MR187255
  10. [10] E. Looijenga: Rational surfaces with an anticanonical cycle. Ann. Math.114 (1981) 267-322. Zbl0509.14035MR632841
  11. [11] I. Nakamura: Inoue-Hirzebruch surfaces and a duality of hyperbolic unimodular singularities. Math. Ann.252 (1980) 221-235. Zbl0425.14010MR593635
  12. [12] I. Nakamura: Duality of cusp singularities in: Complex Analysis of Singularities (R.I.M.S. Symposium, K. Aomoto, organizer)Kyoto (1981). 
  13. [13] V.V. Nikulin: Integral symmetric bilinear forms and some of their applications. Math. USSR Izvestija14 (1980) 103-167. Zbl0427.10014
  14. [14] H. Pinkham: Singularités exceptionnelles, la dualité etrange d'Arnold et les surfaces K-3. C.R. Acad. Sc. Paris, Série A, 284 (1977) 615-618. Zbl0375.14004MR429876
  15. [15] H. Pinkham: Smoothings of the Dpqr singularities, p + q + r = 22. Appendix to Looijenga's paper: the smoothing components of a triangle singularity. Proceedings of the Arcata conference on singularities (1981). Proc. Symp. Pure Math.40 (1983) Part 2, 373-377. Zbl0568.14004MR713261
  16. [16] J.-P. Serre: Cours d'arithmétique. Paris: P.U.F. (1970). Zbl0225.12002
  17. [17] K. Behnke: Infinitesimal deformations of cusp singularities. Math. Ann.265 (1983) 407-422. Zbl0559.14001MR721879
  18. [18] R. Friedman and H. Pinkham: Smoothings of cusp singularities via triangle singularities. To appear in Comp. Math. Zbl0594.14006
  19. [19] T. Oda: On torus embeddings and its applications. TATA Institute Lecture Notes, Bombay (1978). Zbl0417.14043MR546291
  20. [20] P. Wagreich: Singularities of complex surfaces with solvable local fundamental group. Topology11 (1972) 51-72. Zbl0204.56404MR285536
  21. [21] J. Wahl: Smoothings of normal surface singularities. Topology20 (1981) 219-246. Zbl0484.14012MR608599

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.