The birational geometry of R¯g,2 and Prym-canonical divisorial strata

The birational geometry of R¯g,2 and Prym-canonical divisorial strata

We prove that the moduli space of double covers ramified at two points R g , 2 is uniruled for 3 ≤ g ≤ 6 and of general type for g ≥ 16 . Furthermore, we consider Prym-canonical divisorial strata in the moduli space C n R ¯ g parametrizing n -pointed Prym curves, and we compute their classes in Pic...

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Veröffentlicht in:Selecta mathematica (Basel, Switzerland) Switzerland), 2024, Vol.30 (2)
1. Verfasser: Bud, Andrei
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Mathematics and Statistics
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Zusammenfassung:We prove that the moduli space of double covers ramified at two points R g , 2 is uniruled for 3 ≤ g ≤ 6 and of general type for g ≥ 16 . Furthermore, we consider Prym-canonical divisorial strata in the moduli space C n R ¯ g parametrizing n -pointed Prym curves, and we compute their classes in Pic Q ( C n R ¯ g ) .
ISSN:1022-1824
1420-9020
DOI:10.1007/s00029-023-00907-1