Some New Surfaces of General Type with Maximal Picard Number
Abstract
The Picard number ρ(X) of a complex projective manifold X is the rank of its Neron-Severi group. It is bounded above by the Hodge number h11(X). We say that a surface has maximal Picard number if it has the largest possible Picard number, that is, if ρ(X) = h 11(X). The problem of constructing nontrivial examples of such manifolds is particularly interesting in the case when X is a complex projective surface. In this thesis, we use Hodge theory of families to construct examples of complex projective surfaces of general type with maximal Picard number. These surfaces arise as certain families of genus 2 and genus 3 curves fibered over the modular curves and the Shimura curves.
Degree
Ph.D.
Advisors
Arapura, Purdue University.
Subject Area
Mathematics
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