For large ambient dimension n and curve degree e, the moduli space of genus g degree e maps into a smooth degree d hypersurface has at worst terminal singularities.
Non-smoothness of Moduli Spaces of Higher Genus Curves on Low Degree Hypersurfaces
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We show that the moduli space of degree $e$ maps from smooth genus $g \ge 1$ curves to an arbitrary low degree smooth hypersurface is singular when $e$ is large compared to $g$. We also give a lower bound for the dimension of the singular locus.
citation-role summary
background 1
citation-polarity summary
fields
math.AG 1years
2024 1verdicts
CONDITIONAL 1roles
background 1polarities
background 1representative citing papers
citing papers explorer
-
Terminal singularities of the moduli space of curves on low degree hypersurfaces and the circle method
For large ambient dimension n and curve degree e, the moduli space of genus g degree e maps into a smooth degree d hypersurface has at worst terminal singularities.