1,454 research outputs found
A motivic study of generalized Burniat surfaces
Generalized Burniat surfaces are surfaces of general type with and
Euler number obtained by a variant of Inoue's construction method for the
classical Burniat surfaces. I prove a variant of the Bloch conjecture for these
surfaces. The method applies also to the so-called Sicilian surfaces introduced
by Bauer, Catanese and Frapporti. This implies that the Chow motives of all of
these surfaces are finite-dimensional in the sense of Kimura
Rigidity of Spreadings and Fields of Definition
Varieties without deformations are defined over a number field. Several old
and new examples of this phenomenon are discussed such as Bely\u \i\ curves and
Shimura varieties. Rigidity is related to maximal Higgs fields which come from
variations of Hodge structure. Basic properties for these due to P. Griffiths,
W. Schmid, C. Simpson and, on the arithmetic side, to Y. Andr\'e and I. Satake
all play a role. This note tries to give a largely self-contained exposition of
these manifold ideas and techniques, presenting, where possible, short new
proofs for key results.Comment: Accepted for the EMS Surveys in Mathematical Science
On rigidity of locally symmetric spaces
In this note I generalize the classical results of Calabi-Vesentini to
certain non-compact locally symmetric domains, namely those that are quotients
of a hermitian symmetric domain by a neat arithmetic subgroup of the group of
its holomorphic automorphisms.Comment: To be published in the M\"unster Journal of Mathematic
Differential Geometry of the Mixed Hodge Metric
We investigate properties of the Hodge metric of a mixed period domain. In
particular, we calculate its curvature and the curvature of the Hodge bundles.
We also consider when the pull back metric via a period map is K\"ahler.
Several applications in cases of geometric interest are given, such as for
normal functions and biextension bundles.Comment: Ameliorated exposition. Accepted for publication in Communications in
Analysis and Geometr
Abelian Fourfolds of Weil type and certain K3 Double Planes
Double planes branched in 6 lines give a famous example of K3 surfaces. Their
moduli are well understood and related to abelian fourfolds of Weil type. We
compare these two moduli interpretations and in particular divisors on the
moduli spaces. On the K3 side, this is achieved with the help of elliptic
fibrations. We also study the Kuga-Satake correspondence on these special
divisors.Comment: 48 pages, 4 figures; v3: final version with several additions
suggested by the refere
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