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 Generic Torelli theorem for Prym varieties of ramified coverings

2012 ◽  
Vol 148 (4) ◽  
pp. 1147-1170 ◽  
Author(s):  
Valeria Ornella Marcucci ◽  
Gian Pietro Pirola
Keyword(s):  
Moduli Space ◽  
Abelian Varieties ◽  
Branch Points ◽  
Prym Variety ◽  
Prym Varieties ◽  
Torelli Theorem ◽  
Image Position ◽  
Prym Map ◽  
Double Coverings ◽  
Ramified Coverings

AbstractWe consider the Prym map from the space of double coverings of a curve of genus gwithrbranch points to the moduli space of abelian varieties. We prove that 𝒫:ℛg,r→𝒜δg−1+r/2is generically injective ifWe also show that a very general Prym variety of dimension at least 4 is not isogenous to a Jacobian.

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.

The hyperelliptic fibre of the Prym map in genus four

1999 ◽  
pp. 223-229
Author(s):  
L. Hidalgo-Solís ◽  
S. Recillas-Pishmish
Keyword(s):  
Prym Map

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
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