Abstract
We show that the universal plane curve M of fixed degree d ≥ 3 can be seen as a closed subvariety in a certain Simpson moduli space of 1-dimensional sheaves on ℙ2 contained in the stable locus. The universal singular locus of M coincides with the subvariety M′ of M consisting of sheaves that are not locally free on their support. It turns out that the blow up Bl M′ M may be naturally seen as a compactification of M B = M∖M′ by vector bundles (on support).
ACKNOWLEDGMENTS
The author thanks Mario Maican for his valuable comments regarding Section 3. Many thanks as well to an unknown referee for helpful comments, improvements, and suggestions.
Notes
This observation is due to an unknown referee.
Communicated by R. Piene.