Generic injectivity of the Prym map for double ramified coverings

Juan Carlos Naranjo; Angela Ortega

doi:10.1090/tran/7459

Generic injectivity of the Prym map for double ramified coverings

Transactions of the American Mathematical Society ◽

10.1090/tran/7459 ◽

2018 ◽

Vol 371 (5) ◽

pp. 3627-3646 ◽

Cited By ~ 2

Author(s):

Juan Carlos Naranjo ◽

Angela Ortega

Keyword(s):

Prym Map ◽

Ramified Coverings

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Generic Torelli theorem for Prym varieties of ramified coverings

Compositio Mathematica ◽

10.1112/s0010437x12000280 ◽

2012 ◽

Vol 148 (4) ◽

pp. 1147-1170 ◽

Cited By ~ 5

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.

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Convergence of Discrete Period Matrices and Discrete Holomorphic Integrals for Ramified Coverings of the Riemann Sphere

Mathematical Physics Analysis and Geometry ◽

10.1007/s11040-021-09394-2 ◽

2021 ◽

Vol 24 (3) ◽

Author(s):

Alexander I. Bobenko ◽

Ulrike Bücking

Keyword(s):

Error Estimate ◽

Branch Point ◽

Riemann Surfaces ◽

Riemann Sphere ◽

Holomorphic Functions ◽

Convergence Result ◽

Edge Length ◽

Ramified Covering ◽

Compact Riemann Surfaces ◽

Ramified Coverings

AbstractWe consider the class of compact Riemann surfaces which are ramified coverings of the Riemann sphere $\hat {\mathbb {C}}$ ℂ ̂ . Based on a triangulation of this covering we define discrete (multivalued) harmonic and holomorphic functions. We prove that the corresponding discrete period matrices converge to their continuous counterparts. In order to achieve an error estimate, which is linear in the maximal edge length of the triangles, we suitably adapt the triangulations in a neighborhood of every branch point. Finally, we also prove a convergence result for discrete holomorphic integrals for our adapted triangulations of the ramified covering.

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