What question did this study set out to answer?

The aim is to analyze the Prym-Brill-Noether variety and its implications for moduli spaces of Prym curves.

February 8, 2026Open Access

The Class of the Prym-Brill-Noether Divisor

Puntos clave

The aim is to analyze the Prym-Brill-Noether variety and its implications for moduli spaces of Prym curves.
Studied the Prym-Brill-Noether variety associated with Prym curves.
Parametrized Prym curves with nonempty varieties in moduli space.
Computed coefficients of relevant divisor classes in Picard groups.
Examined irreducibility of a strongly Brill-Noether divisor.
Identified key coefficients in the class of the divisor in Picard groups.
Showed the irreducibility of the Brill-Noether divisor in moduli space.
Concluded that the moduli space of specific Prym curves is of general type.

Resumen

Abstract For r 3 and g= r (r+1) 2, we study the Prym-Brill-Noether variety Vʳ (C, ) associated to Prym curves C,. The locus Rgʳ in Rg parametrizing Prym curves (C, ) with nonempty Vʳ (C, ) is a divisor. We compute some key coefficients of the class {R}gʳ in Pic ₐ ({R}g). Furthermore, we examine a strongly Brill-Noether divisor in {M}₆-₁, ₂: we show its irreducibility and compute some of its coefficients in Pic ₐ ({M}₆-₁, ₂). As a consequence of our results, the moduli space R₁₄, ₂ is of general type.

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