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Transactions of the American Mathematical Society

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On the GIT quotient space of quintic surfaces


Author: Patricio Gallardo
Journal: Trans. Amer. Math. Soc. 371 (2019), 4251-4276
MSC (2010): Primary 14J10, 14L24
DOI: https://doi.org/10.1090/tran/7493
Published electronically: October 2, 2018
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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.


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Additional Information

Patricio Gallardo
Affiliation: Department of Mathematics, Washington University at St. Louis, 1 Brookings Drive, St. Louis, Missouri 63130
Email: pgallardocandela@wustl.edu

DOI: https://doi.org/10.1090/tran/7493
Keywords: Geometric invariant theory, quintic surfaces
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
Article copyright: © Copyright 2018 American Mathematical Society