Transactions of the American Mathematical Society

Author(s): Radu Laza
Journal: Trans. Amer. Math. Soc. 361 (2009), 2109-2161.
MSC (2000): Primary 14J17, 14B07, 32S25; Secondary 14L24
Posted: November 12, 2008
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Abstract: We study the deformations of the minimally elliptic surface singularity $N_{16}$ . A standard argument reduces the study of the deformations of $N_{16}$ to the study of the moduli space of pairs

consisting of a plane quintic curve and a line. We construct this moduli space in two ways: via the periods of

surfaces and by using geometric invariant theory (GIT). The GIT construction depends on the choice of the linearization. In particular, for one choice of linearization we recover the space constructed via

surfaces and for another we obtain the full deformation space of $N_{16}$ . The two spaces are related by a series of explicit flips. In conclusion, by using the flexibility given by GIT and the standard tools of Hodge theory, we obtain a good understanding of the deformations of $N_{16}$ .

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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 14J17, 14B07, 32S25, 14L24

Radu Laza
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Email: rlaza@umich.edu

DOI: 10.1090/S0002-9947-08-04660-6
PII: S 0002-9947(08)04660-6
Received by editor(s): August 28, 2006
Received by editor(s) in revised form: May 21, 2007
Posted: November 12, 2008
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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