Boundedness of the period maps and global Torelli theorem

2016 ◽  
Vol 60 (6) ◽  
pp. 1029-1046 ◽  
Author(s):  
KeFeng Liu ◽  
Yang Shen
Keyword(s):  
Torelli Theorem

The generic Torelli theorem for the Prym map

1982 ◽  
Vol 67 (3) ◽  
pp. 473-490 ◽  
Author(s):  
Robert Friedman ◽  
Roy Smith
Keyword(s):  
Torelli Theorem ◽  
Prym Map

scholarly journals FUJITA DECOMPOSITION AND HODGE LOCI

2018 ◽  
Vol 19 (4) ◽  
pp. 1389-1408 ◽  
Author(s):  
Paola Frediani ◽  
Alessandro Ghigi ◽  
Gian Pietro Pirola
Keyword(s):  
Totally Geodesic ◽  
Exterior Power ◽  
Period Map ◽  
Flat Part ◽  
Torelli Theorem

This paper contains two results on Hodge loci in $\mathsf{M}_{g}$. The first concerns fibrations over curves with a non-trivial flat part in the Fujita decomposition. If local Torelli theorem holds for the fibers and the fibration is non-trivial, an appropriate exterior power of the cohomology of the fiber admits a Hodge substructure. In the case of curves it follows that the moduli image of the fiber is contained in a proper Hodge locus. The second result deals with divisors in $\mathsf{M}_{g}$. It is proved that the image under the period map of a divisor in $\mathsf{M}_{g}$ is not contained in a proper totally geodesic subvariety of $\mathsf{A}_{g}$. It follows that a Hodge locus in $\mathsf{M}_{g}$ has codimension at least 2.

A Torelli theorem for moduli spaces of principal bundles on curves defined over ℝ

2017 ◽  
Vol 28 (06) ◽  
pp. 1750049
Author(s):  
Indranil Biswas ◽  
Olivier Serman
Keyword(s):  
Algebraic Group ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Isomorphism Class ◽  
Projective Curve ◽  
Real Numbers ◽  
Principal Bundles ◽  
Smooth Projective Curve ◽  
Simple Factor ◽  
Torelli Theorem

Let [Formula: see text] be a geometrically irreducible smooth projective curve, of genus at least three, defined over the field of real numbers. Let [Formula: see text] be a connected reductive affine algebraic group, defined over [Formula: see text], such that [Formula: see text] is nonabelian and has one simple factor. We prove that the isomorphism class of the moduli space of principal [Formula: see text]-bundles on [Formula: see text] determine uniquely the isomorphism class of [Formula: see text].

A New Proof of the Global Torelli Theorem for K3 Surfaces

1984 ◽  
Vol 120 (2) ◽  
pp. 237 ◽  
Author(s):  
Robert Friedman
Keyword(s):  
K3 Surfaces ◽  
Torelli Theorem

scholarly journals Minimal Siegel modular threefolds

1998 ◽  
Vol 123 (3) ◽  
pp. 461-485 ◽  
Author(s):  
VALERI GRITSENKO ◽  
KLAUS HULEK
Keyword(s):  
Difficult Problem ◽  
Kodaira Dimension ◽  
Abelian Surfaces ◽  
Starting Point ◽  
Hilbert Modular Surfaces ◽  
Hilbert Modular ◽  
Kummer Surfaces ◽  
Torelli Theorem ◽  
Ramification Locus ◽  
Modular Threefolds

The starting point of this paper is the maximal extension Γ*t of Γt, the subgroup of Sp4(ℚ) which is conjugate to the paramodular group. Correspondingly we call the quotient [Ascr ]*t=Γ*t\ℍ2 the minimal Siegel modular threefold. The space [Ascr ]*t and the intermediate spaces between [Ascr ]t=Γt\ℍ2 which is the space of (1, t)-polarized abelian surfaces and [Ascr ]*t have not yet been studied in any detail. Using the Torelli theorem we first prove that [Ascr ]*t can be interpreted as the space of Kummer surfaces of (1, t)-polarized abelian surfaces and that a certain degree 2 quotient of [Ascr ]t which lies over [Ascr ]*t is a moduli space of lattice polarized K3 surfaces. Using the action of Γ*t on the space of Jacobi forms we show that many spaces between [Ascr ]t and [Ascr ]*t possess a non-trivial 3-form, i.e. the Kodaira dimension of these spaces is non-negative. It seems a difficult problem to compute the Kodaira dimension of the spaces [Ascr ]*t themselves. As a first necessary step in this direction we determine the divisorial part of the ramification locus of the finite map [Ascr ]t→[Ascr ]*t. This is a union of Humbert surfaces which can be interpreted as Hilbert modular surfaces.

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