THE CLASS OF THE PRYM-BRILL-NOETHER DIVISOR
Abstract
Abstract For $r\geq 3$ and $g= \frac {r(r+1)}{2}$ , we study the Prym-Brill-Noether variety $V^r(C,\eta )$ associated to Prym curves $[C,\eta ]$ . The locus $\mathcal {R}_g^r$ in $\mathcal {R}_g$ parametrizing Prym curves $(C, \eta )$ with nonempty $V^r(C,\eta )$ is a divisor. We compute some key coefficients of the class $[\overline {\mathcal {R}}_g^r]$ in $\mathrm {Pic}_{\mathbb {Q}}(\overline {\mathcal {R}}_g)$ . Furthermore, we examine a strongly Brill-Noether divisor in $\overline {\mathcal {M}}_{g-1,2}$ : we show its irreducibility and compute some of its coefficients in $\mathrm {Pic}_{\mathbb {Q}}(\overline {\mathcal {M}}_{g-1,2})$ . As a consequence of our results, the moduli space $\mathcal {R}_{14,2}$ is of general type.
Fields of Study & Subjects
Advanced Topics in Algebra
Nonlinear Waves and Solitons
Advanced Algebra and Geometry
Publication details
- Journal / source
- Journal of the Institute of Mathematics of Jussieu
- Publisher
- Cambridge University Press (CUP)
- Volume
- 25
- Issue
- 2
- Pages
- 1281–1310
- Publication date
- 5 February 2026
- Language
- EN