scholarly journals Torelli Theorem Via Fourier-Mukai Transform

2001 ◽  
pp. 127-132 ◽  
Author(s):  
A. Beilinson ◽  
A. Polishchuk
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.

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

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
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