Monodromy and Picard-Fuchs equations for families of K 3 -surfaces and elliptic curves

C. Peters

Annales scientifiques de l'École Normale Supérieure (1986)

  • Volume: 19, Issue: 4, page 583-607
  • ISSN: 0012-9593

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Peters, C.. "Monodromy and Picard-Fuchs equations for families of $K3$-surfaces and elliptic curves." Annales scientifiques de l'École Normale Supérieure 19.4 (1986): 583-607. <http://eudml.org/doc/82188>.

@article{Peters1986,
author = {Peters, C.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {monodromy representation of the variations of Hodge structure; Gauss- Manin connection; Picard-Fuchs equations; K3 surfaces; 1-dimensional families of abelian surfaces},
language = {eng},
number = {4},
pages = {583-607},
publisher = {Elsevier},
title = {Monodromy and Picard-Fuchs equations for families of $K3$-surfaces and elliptic curves},
url = {http://eudml.org/doc/82188},
volume = {19},
year = {1986},
}

TY - JOUR
AU - Peters, C.
TI - Monodromy and Picard-Fuchs equations for families of $K3$-surfaces and elliptic curves
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1986
PB - Elsevier
VL - 19
IS - 4
SP - 583
EP - 607
LA - eng
KW - monodromy representation of the variations of Hodge structure; Gauss- Manin connection; Picard-Fuchs equations; K3 surfaces; 1-dimensional families of abelian surfaces
UR - http://eudml.org/doc/82188
ER -

References

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  1. [B] A. BEAUVILLE, Les familles stables de courbes elliptiques sur P2 admettant quatre fibres singulières (C. R. Acad. Sc., Paris, T. 294, 1982, p. 657). Zbl0504.14016MR83h:14008
  2. [Ba-P] W. BARTH and C. PETERS, Automorphisms of Enriques Surfaces (Invent. Math., Vol. 73, 1983, pp. 383-411). Zbl0518.14023MR85g:14052
  3. [B-B] W. L. BAILY, Jr and A. BOREL, Compactification of arithmetic quotients of bounded symmetric domains (Ann. Math., Vol. 84, 1966, pp. 422-528). Zbl0154.08602MR35 #6870
  4. [B-P] F. BEUKERS and C. PETERS, A family of K3-surfaces and ζ (3) (Journal für d.r.u. angew. Math., Vol. 351, 1984, pp. 42-54). Zbl0541.14007MR87h:11056
  5. [B-P-V] W. BARTH, C. PETERS and A. VAN DE VEN, Compact Complex Surfaces, Ergebnisse der Math. 3 Folge, Band 4, Springer-Verlag, 1984. Zbl0718.14023MR86c:32026
  6. [D] P. DELIGNE, Équations différentielles à points singuliers réguliers (Lect. Notes Math., 163, Springer-Verlag, 1970). Zbl0244.14004MR54 #5232
  7. [K-F] F. KLEIN and R. FRICKE, Vorlesungen über die Theorie der elliptischen Modulfunctionen, I, Teubner, Leipzig, 1890 ; II, Teubner, Leipzig, 1892. JFM22.0455.02
  8. [M] D. R. MORRISON, Some remarks on the moduli of K3-surfaces. In : Classification of algebraic and analytic manifolds, Progress in Math., 39, Birkhöuser Verlag, 1983, pp. 303-332. Zbl0526.14025MR85h:32038
  9. [M2] D. R. MORRISON, On K3-surfaces with large Picard number (Invent. Math., Vol. 75, 1984, pp. 105-121). Zbl0509.14034MR85j:14071
  10. [N] V. NIKULIN, Integral symmetric bilinear forms and some of their applications (Izv. Akad. Nauk S.S.S.R., Vol. 43, 1979, pp. 111-177 ; Math. U.S.S.R. Izvestija, Vol. 14, 1980, pp. 103-167). Zbl0408.10011
  11. [P] I. PIATEČKII-SHAPIRO, Geometry of classical domains and automorphic functions (Russian), Fizmatgiz, Moscow, 1961. French transl. Dunod, Paris, 1966. 
  12. [P-S] C. PETERS and J. STEENBRINK, Infinitesimal variations of Hodge structure and the generic Torelli problem for projective hypersurfaces, In : Classification of algebraic and analytic manifolds, Progress in Math., 39, Birkhöuser Verlag, 1983, pp. 399-463. Zbl0523.14009MR85j:32036
  13. [R] H. RADEMACHER, Topics in analytic number theory (Grundlehren Math. Wiss., 169, Springer-Verlag, 1973). Zbl0253.10002MR51 #358
  14. [R-S] R. REMMERT and K. STEIN, Über die wesentlichen Singularitöten analytischer Mengen (Math. Ann., Vol. 126, 1953, pp. 263-306). Zbl0051.06303MR15,615e
  15. [S] W. SCHMID, Variation of Hodge structure : the singularities of the period mapping (Invent. Math., Vol. 22, 1973, pp. 211-319). Zbl0278.14003MR52 #3157
  16. [S1] T. SHIODA, On elliptic modular surfaces (J. Math. Soc. Japan, Vol. 24, 1972, pp. 20-59). Zbl0226.14013MR55 #2927
  17. [S2] T. SHIODA, The period map of abelian surfaces (J. Fac. Sc. Univ. Tokyo, Vol. 25, 1978, pp. 47-59). Zbl0405.14021MR58 #690
  18. [S-B] J. STIENSTRA and F. BEUKERS, On the Picard-Fuchs equation and the formal Brauer group of certain elliptic K3-surfaces (Math. Ann., Vol. 271, 1985). Zbl0539.14006MR86j:14045

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