The Divisors of Prym Semicanonical Pencils

Abstract

Abstract In the moduli space ${{\mathcal {R}}}_g$ of double étale covers of curves of a fixed genus $g$, the locus of covers of curves with a semicanonical pencil decomposes as the union of two divisors—${{\mathcal {T}}}^e_g$ and ${{\mathcal {T}}}^o_g$. Adapting arguments of Teixidor for the divisor of curves having a semicanonical pencil, we prove that both divisors are irreducible and compute their divisor classes in the Deligne–Mumford compactification ${\overline {{\mathcal {R}}}}_g$.