On the GIT quotient space of quintic surfaces
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Abstract:
We describe the GIT compactification for the moduli space of smooth quintic surfaces in ${\mathbb {P}^{3}}$. In particular, we show that a normal quintic surface with at worst isolated double points or minimal elliptic singularities is stable. We also describe the boundary of the GIT quotient, and we discuss the stability of the nonnormal surfaces.References
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Additional Information
- Patricio Gallardo
- Affiliation: Department of Mathematics, Washington University at St. Louis, 1 Brookings Drive, St. Louis, Missouri 63130
- MR Author ID: 1228133
- Email: pgallardocandela@wustl.edu
- Received by editor(s): May 1, 2015
- Received by editor(s) in revised form: July 21, 2016, September 21, 2017, November 29, 2017, and December 6, 2017
- Published electronically: October 2, 2018
- Additional Notes: The author was partially supported by the NSF grant DMS-125481 (PI: R. Laza), and by the W. Burghardt Turner Fellowship
- © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 371 (2019), 4251-4276
- MSC (2010): Primary 14J10, 14L24
- DOI: https://doi.org/10.1090/tran/7493
- MathSciNet review: 3917222