195,318 research outputs found
A fibered power theorem for pairs of log general type
Let be a stably family with log canonical general fiber. We
prove that, after a birational modification of the base ,
there is a morphism from a high fibered power of the family to a pair of log
general type. If in addition the general fiber is openly canonical, then there
is a morphism from a high fibered power of the original family to a pair openly
of log general type.Comment: Exposition has been greatly improved. Version to appear in Algebra &
Number Theor
On the equidistribution of some Hodge loci
We prove the equidistribution of the Hodge locus for certain non-isotrivial,
polarized variations of Hodge structure of weight with over
complex, quasi-projective curves. Given some norm condition, we also give an
asymptotic on the growth of the Hodge locus. In particular, this implies the
equidistribution of elliptic fibrations in quasi-polarized, non-isotrivial
families of surfaces.Comment: 33 pages. To appear in Journal f\"ur die reine und angewandte
Mathematik (Crelles Journal
Viehweg's hyperbolicity conjecture for families with maximal variation
We use the theory of Hodge modules to construct Viehweg-Zuo sheaves on the
base spaces of families with maximal variation and fibers of general type, or
more generally whose geometric generic fiber has a good minimal model. We
deduce Viehweg's hyperbolicity conjecture in this context, namely the fact that
the base spaces of such families are of log general type. This is approached as
part of a general problem of identifying what spaces can support Hodge
theoretic objects with certain positivity properties.Comment: 28 pages; final version with a few expository improvements, to appear
in Invent. Mat
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