Abstract For even genus $$g=2i\ge 4$$ g=2i≥4 and the length $$g-1$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">g-1 part...

In this paper we construct Shimura subvarieties of dimension bigger than one the moduli space polarised abelian varieties a given dimension, which are generically contained in Pym loci (ramified) double covers. The idea is to adapt techniques already used curves Prym higher dimensional case, namely use families Galois covers projective line. case treated detail, since it possible make explicit ...

A well-known conjecture asserts that the mapping class group of a surface (possibly with punctures/boundary) does not virtually surject onto Z if the genus of the surface is large. We prove that if this conjecture holds for some genus, then it also holds for all larger genera. We also prove that if there is a counterexample to this conjecture, then there must be a counterexample of a particular...

In the moduli space R g $\mathcal {R}_g$ of double étale covers curves a fixed genus g, locus formed by with semicanonical pencil consists two irreducible divisors T e {T}^e_g$ and o {T}^o_g$ . We study Prym map on these divisors, which shows significant differences between them has rich geometry in cases low genus. particular, analysis 5 {T}^o_5$ enumerative consequences for lines cubic threef...