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Bounds for the number of moduli for irregular varieties of general type

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Abstract

LetX be a minimal surface of general type and M (X) the set of equivalence classes of complex structures on the differentiable manifold underlyingX; denoting byM x the dimension of M(X) at [X], the point corresponding to the complex structure ofX we consider the problem of finding an upper bound forM x in terms of the basic numerical invariants ofX. The main result is the Castelunovo's bound:M x≤Pg(X)+2q(X) for certain irregular surfaces. We also generalize the above bound to an arbitrary dimension.

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  1. Department of Mathematics, University of Oklahoma, 601 Elm Ave., Room 423, 73019, Norman, OK

    Igor Reider

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  1. Igor Reider
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Reider, I. Bounds for the number of moduli for irregular varieties of general type. Manuscripta Math 60, 221–233 (1988). https://doi.org/10.1007/BF01161932

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  • DOI: https://doi.org/10.1007/BF01161932

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