Root systems and Jacobi forms

Klaus Wirthmüller

Compositio Mathematica (1992)

  • Volume: 82, Issue: 3, page 293-354
  • ISSN: 0010-437X

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Wirthmüller, Klaus. "Root systems and Jacobi forms." Compositio Mathematica 82.3 (1992): 293-354. <http://eudml.org/doc/90155>.

@article{Wirthmüller1992,
author = {Wirthmüller, Klaus},
journal = {Compositio Mathematica},
keywords = {invariant theory; modular group; Weyl group; root system; toroidal embedding; Jacobi forms; polynomial algebra; deformation of fat points},
language = {eng},
number = {3},
pages = {293-354},
publisher = {Kluwer Academic Publishers},
title = {Root systems and Jacobi forms},
url = {http://eudml.org/doc/90155},
volume = {82},
year = {1992},
}

TY - JOUR
AU - Wirthmüller, Klaus
TI - Root systems and Jacobi forms
JO - Compositio Mathematica
PY - 1992
PB - Kluwer Academic Publishers
VL - 82
IS - 3
SP - 293
EP - 354
LA - eng
KW - invariant theory; modular group; Weyl group; root system; toroidal embedding; Jacobi forms; polynomial algebra; deformation of fat points
UR - http://eudml.org/doc/90155
ER -

References

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  2. [Bernshtein and Shvartsman] I.N. Bernshtein and O.V. Shvartsman, Chevalley's theorem for complex crystallographic Coxeter groups, Funct. Anal. Appl.12 (1978), 308-310. Zbl0458.32017
  3. [Bourbaki] N. Bourbaki, Groupes et Algebres de Lie, Ch. 4, 5, 6, Masson, 1981. Zbl0483.22001MR647314
  4. [Demazure 1] M. Demazure, Sous-groupes algébriques de rang maximum du groupe de Dremona, Ann. Sci. Ecole Norm. Sup.3 (1970). Zbl0223.14009MR284446
  5. [Demazure 2] M. Demazure, Surfaces de Del Pezzo, in: Séminaire sur les singularités des surfaces, Springer Lecture Notes in Math. 777 (1980). Zbl0444.14024
  6. [Eichler and Zagier] M. Eichler and D. Zagier, The Theory of Jacobi Forms, Birkhäuser, 1985. Zbl0554.10018MR781735
  7. [Gunning] R.C. Gunning, Lectures on Modular Forms, Annals of Math. Studies48, Princeton University Press, 1962. Zbl0178.42901MR132828
  8. [Kac] V.G. Kac, Infinite Dimensional Lie Algebras, Birkhäuser, 1983. MR739850
  9. [Kac and Peterson] V. Kac and D. Peterson, Infinite-dimensional Lie algebras, theta-functions and modular forms, Adv. in Math.53 (1984), 125-264. Zbl0584.17007MR750341
  10. [Kempf et al] G. Kempf et al., Toroidal Embeddings I, Springer Lecture Notes in Math. 339 (1973). Zbl0271.14017MR335518
  11. [Looijenga 1] E. Looijenga, Root systems and elliptic curves, Invent. Math.38 (1976), 17-32. Zbl0358.17016MR466134
  12. [Looijenga 2] E. Looijenga, On the semi-universal deformation of a simple-elliptic hypersurface singularity II, Topology17 (1978), 23-40. Zbl0392.57013MR492380
  13. [Looijenga 3] E. Looijenga, Invariant theory for generalized root systems, Invent. Math.61 (1980), 1-32. Zbl0436.17005MR587331
  14. [Mumford] D. Mumford, Abelian Varieties, Tata Institute of Fundamental Research Studies in Mathematics, Oxford University Press, 1970. Zbl0223.14022MR282985
  15. [Namikawa] Y. Namikawa, Toroidal degeneration of abelian varieties, in: Complex Analysis and Algebraic Geometry, Tokio, Cambridge University Press, 1977. Zbl0351.14020MR457436
  16. [Saito 1] K. Saito, Families of line bundles over elliptic curves, Kyoto University, 1988 (preprint RIMS-626). 
  17. [Saito 2] K. Saito, Extended affine root systems II, Kyoto University, 1988 (preprint RIMS-633). 
  18. [Siu and Trautmann] Y.-T. Siu and G. Trautmann, Gap-Sheaves and Extension of Coherent Analytic Subsheaves, Springer Lecture Notes in Math. 172 (1971). Zbl0208.10403MR287033
  19. [Wirthmüller 1] K. Wirthmüller, Deformations of fat points of Boardman type 2, 0, Math. Ann.259 (1982), 519-539. Zbl0469.32009MR660046
  20. [Wirthmüller 2] K. Wirthmüller, Torus embeddings and deformations of simple singularities of space curves, Acta Math.157 (1986), 159-241. Zbl0635.14015MR857673

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