|
Coupled contact systems and rigidity of maximal dimensional variations of Hodge structure
Author(s):
Richárd
Mayer
Journal:
Trans. Amer. Math. Soc.
352
(2000),
2121-2144.
MSC (1991):
Primary 14C30
Posted:
July 26, 1999
MathSciNet review:
1624194
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
In this article we prove that locally Griffiths' horizontal distribution on the period domain is given by a generalized version of the familiar contact differential system. As a consequence of this description we obtain strong local rigidity properties of maximal dimensional variations of Hodge structure. For example, we prove that if the weight is odd (greater than one) then there is a unique germ of maximal dimensional variation of Hodge structure through every point of the period domain. Similar results hold if the weight is even with the exception of one case.
References:
- [A]
- V. I. Arnold, Mathematical Methods of Classical Mechanics, Graduate Text in Mathematics, Springer-Verlag, 1978. MR 57:14033h
- [B]
- R. L. Bryant et al. Exterior differential systems, Springer-Verlag, New York, 1991. MR 92h:58007
- [C1]
- J. A. Carlson, Bounds on the dimension of a variation of Hodge structure, Trans. Amer. Math. Soc., 294 (1986), pp. 1-99. MR 87j:14010a
- [C2]
- J. A. Carlson, Hypersurface variations are maximal II, Trans. Amer. Math. Soc., 323 (1991), pp. 1-99. MR 91c:14013
- [C-D]
- J. A. Carlson and Ron Donagi, Hypersurface variations are maximal I, Invent. Math., 89 (1987), pp. 1-99. MR 88i:14005
- [C-S]
- J. A. Carlson and C. Simpson, Shimura varieties of weight two Hodge structures, in Lecture Notes in Mathematics 1246, Springer, Berlin, 1987, pp. 1-15. MR 88j:14013
- [C-K-T]
- J. A. Carlson, A. Kasparian and D. Toledo, Variations of Hodge structure of maximal dimension, Duke Mathematical Journal, 58 (1989), pp. 1-99. MR 90h:14015
- [G1]
- P. Griffiths, Periods of integrals on algebraic manifolds I, II, Amer. J. Math., 90 (1968), pp. 1-99, 805-865. MR 37:5215; MR 38:2146
- [G2]
- P. Griffiths, Topics in transcendental algebraic geometry, Annals of Mathematics Studies 106, Princeton University Press, Princeton, NJ, 1984. MR 86b:14004
- [S]
- W. Schmid, Variations of Hodge Structure: the Singularities of the Period Mapping, Invent. Math., 22 (1973), pp. 211-319. MR 52:3157
- [W]
- F. W. Warner, Foundations of Differentiable Manifolds and Lie Groups, Graduate Text in Mathematics, Springer, New York, 1983. MR 84k:58001
Similar Articles:
Retrieve articles in Transactions of the American Mathematical
Society
with
MSC (1991):
14C30
Retrieve articles in all Journals with
MSC (1991):
14C30
Additional Information:
Richárd
Mayer
Affiliation:
Department of Mathematics, University of Massachusetts, Amherst, Massachusetts 01003
Email:
mayer@math.umass.edu
DOI:
10.1090/S0002-9947-99-02395-8
PII:
S 0002-9947(99)02395-8
Received by editor(s):
December 5, 1997
Posted:
July 26, 1999
Copyright of article:
Copyright
2000,
American Mathematical Society
|
