# Notes on fundamental algebraic supergeometry. Hilbert and Picard superschemes.

@article{Bruzzo2020NotesOF, title={Notes on fundamental algebraic supergeometry. Hilbert and Picard superschemes.}, author={Ugo Bruzzo and Daniel Hern{\'a}ndez Ruip{\'e}rez and Alexander Polishchuk}, journal={arXiv: Algebraic Geometry}, year={2020} }

These notes aim at providing a complete and systematic account of some foundational aspects of algebraic supergeometry, namely, the extension to the geometry of superschemes of many classical notions, techniques and results that make up the general backbone of algebraic geometry, most of them originating from Grothendieck's work. In particular, we extend to algebraic supergeometry such notions as projective and proper morphisms, finiteness of the cohomology, vector and projective bundles…

## 2 Citations

### The moduli space of stable supercurves and its canonical line bundle

- Mathematics
- 2020

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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