Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-28T13:17:39.309Z Has data issue: false hasContentIssue false
  • English
  • Français

Geometric invariant theory of linear systems

Published online by Cambridge University Press:  24 October 2008

C. T. C. Wall
C. T. C. Wall
Affiliation:
Department of Pure Mathematics, The University, Liverpool L69 3BX
Get access Rights & Permissions [Opens in a new window]

Extract

In considering the geometric invariant theory of linear systems (pencils, nets, …) of geometrical objects (quadrics, cubic curves, binary forms,…) there are several ways to apply the basic theory. The object of this note is to point out the equivalence of different approaches and to apply this remark to a number of special cases.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 93 , Issue 1 , January 1983 , pp. 57 - 62
Copyright
Copyright © Cambridge Philosophical Society 1983

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(0)Hsiang, W.-C. and Hsiang, W.-Y.Differentiable actions of compact connected classical groups II. Ann. of Math. 92 (1970), 189–223.CrossRefGoogle Scholar
(1)Luna, D.Slices étales. Bull Soc. Math. France, Mémoire 33 (1973), 81–105.Google Scholar
(2)Miranda, R.On the stability of pencils of cubic curves. Amer. J. Math. 102 (1980), 1177–1202.CrossRefGoogle Scholar
(3)Mumford, D.Geometric invariant theory (Springer-Verlag, 1965).CrossRefGoogle Scholar
(4)Mumford, D.Stability of projective varieties. Enseignement Math. 23 (1977), 39–110.Google Scholar
(5)Newstead, P. E. Introduction to moduli problems and orbit spaces. Tata Institute Notes vol. 51 (Springer-Verlag, 1978).Google Scholar
(6)Newstead, P. E.Invariants of pencils of binary cubics. Math. Proc. Cambridge Philos. Soc. 89 (1981), 201–210.CrossRefGoogle Scholar
(7)Orlik, P. and Wagreich, P.Isolated singularities of algebraic surfaces with C* action. Ann. of Math. 93 (1971), 205–228.CrossRefGoogle Scholar
(8)Wall, C. T. C.Nets of conics. Math. Proc. Cambridge Philos. Soc. 81 (1977), 351–364.CrossRefGoogle Scholar
(9)Wall, C. T. C.Nets of quadrics and theta-characteristics of singular curves. Philos. Trans. Roy. Soc. London Ser. A 289 (1978), 229–269.Google Scholar