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Klein coverings over hyperelliptic genus 3 curves
Paweł Borówka, Angela Ortega
We characterize the moduli space of étale Klein coverings (i.e. Galois with deck group ) of hyperelliptic curves of genus 3. We prove that the Prym map on each comp…
Finiteness and injectivity of Prym maps for cyclic coverings
Paweł Borówka, Juan Carlos Naranjo, Angela Ortega +1
The structure of the Prym map for coverings of degrees is mostly unknown. Only recently, under mild numerical assumptions, a generic injectivity of the Prym maps for étal…
Pryms of coverings of genus 2 curves
Paweł Borówka, Anatoli Shatsila
We study unramified Galois coverings of genus 2 curves and the corresponding Prym varieties and Prym maps. In particular, we prove that any such…
A note on dual abelian varieties
Aleksandra Borówka, Paweł Borówka
For any non-principal polarisation , we explicitly construct -polarised abelian variety , such that its dual abelian variety is not (abstractly) isomorphic to . For $\d…
Involutions on hyperelliptic curves and Prym maps
Paweł Borówka, Angela Ortega
We investigate the geometry of smooth hyperelliptic curves that possess additional involutions, especially from the point of view of the Prym theory. Our main result is the injecti…
Non-simple polarised abelian surfaces and genus 3 curves with completely decomposable Jacobians
Robert Auffarth, Paweł Borówka
We study the space of non-simple polarised abelian surfaces. Specifically, we describe for which pairs the locus of polarised abelian surfaces of type that contain…
Klein coverings of genus 2 curves
Paweł Borówka, Angela Ortega
We investigate the geometry of étale coverings of smooth complex genus 2 curves with the monodromy group isomorphic to the Klein four-group. There are two cases, isotropic an…
Hyperelliptic genus 4 curves on abelian surfaces
Paweł Borówka, G. K. Sankaran
We study smooth curves on abelian surfaces, especially for genus 4, when the complementary subvariety in the Jacobian is also a surface. We show that up to translation there is exa…