Details
| Original language | English |
|---|---|
| Article number | 80 |
| Journal | GEOMETRIAE DEDICATA |
| Volume | 217 |
| Issue number | 5 |
| Early online date | 7 Jul 2023 |
| Publication status | Published - Oct 2023 |
Abstract
We construct a smooth Deligne–Mumford compactification for the moduli space of curves with an m-tuple of spin structures using line bundles on quasi-stable curves as limiting objects, as opposed to line bundles on stacky curves. For all m, we give a combinatorial description of the local structure of the corresponding coarse moduli spaces. We also classify all irreducible and connected components of the resulting moduli spaces of multiple-spin curves.
Keywords
- Compactification, Moduli, Roots of line bundles, Spin curves, Theta-characteristics
ASJC Scopus subject areas
- Mathematics(all)
- Geometry and Topology
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In: GEOMETRIAE DEDICATA, Vol. 217, No. 5, 80, 10.2023.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A compactification of the moduli space of multiple-spin curves
AU - Sertöz, Emre Can
N1 - Funding Information: It is my pleasure to thank my adviser Gavril Farkas for generously sharing his insight into research as well as giving me financial and academic support during the course of my PhD. I would like to thank my co-adviser Gerard van der Geer for numerous discussions during my stay in Amsterdam. In addition, thanks to Lenny Taelman and David Holmes for providing helpful suggestions at key moments. Special thanks go to Fabio Tonini for helping me with stacks and to Klaus Altmann for helping me extend my scholarship. Finally, I thank Özde Bayer Sertöz for the help with the picture. This research constitutes a chapter in my PhD thesis. My PhD was funded by the Berlin Mathematical School and Graduiertenkolleg 1800 of the Deutsche Forschungsgemeinschaft. I am grateful to the referee for their careful reading and insightful comments.
PY - 2023/10
Y1 - 2023/10
N2 - We construct a smooth Deligne–Mumford compactification for the moduli space of curves with an m-tuple of spin structures using line bundles on quasi-stable curves as limiting objects, as opposed to line bundles on stacky curves. For all m, we give a combinatorial description of the local structure of the corresponding coarse moduli spaces. We also classify all irreducible and connected components of the resulting moduli spaces of multiple-spin curves.
AB - We construct a smooth Deligne–Mumford compactification for the moduli space of curves with an m-tuple of spin structures using line bundles on quasi-stable curves as limiting objects, as opposed to line bundles on stacky curves. For all m, we give a combinatorial description of the local structure of the corresponding coarse moduli spaces. We also classify all irreducible and connected components of the resulting moduli spaces of multiple-spin curves.
KW - Compactification
KW - Moduli
KW - Roots of line bundles
KW - Spin curves
KW - Theta-characteristics
UR - http://www.scopus.com/inward/record.url?scp=85164171095&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1701.02303
DO - 10.48550/arXiv.1701.02303
M3 - Article
AN - SCOPUS:85164171095
VL - 217
JO - GEOMETRIAE DEDICATA
JF - GEOMETRIAE DEDICATA
SN - 0046-5755
IS - 5
M1 - 80
ER -