The moduli space of stable supercurves and its canonical line bundle
Giovanni Felder, David Kazhdan, Alexander Polishchuk
TL;DR
This paper establishes that the moduli space of stable supercurves with punctures is a smooth proper Deligne-Mumford stack and explores an analog of Mumford's isomorphism for its canonical line bundle.
Contribution
It proves the smoothness and properness of the moduli stack of stable supercurves and develops an analog of Mumford's isomorphism in this context.
Findings
The moduli space is a smooth proper DM stack.
An analog of Mumford's isomorphism is established for the canonical line bundle.
Foundational results for the geometry of supercurves are provided.
Abstract
We prove that the moduli of stable supercurves with punctures is a smooth proper DM stack and study an analog of the Mumford's isomorphism for its canonical line bundle.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Black Holes and Theoretical Physics