Log canonical models and variation of GIT for genus 4 canonical curves

Casalaina-Martin, Sebastian; Jensen, David; Laza, Radu

doi:10.1090/S1056-3911-2014-00636-6

Log canonical models and variation of GIT for genus $4$ canonical curves

Authors: Sebastian Casalaina-Martin, David Jensen and Radu Laza
Journal: J. Algebraic Geom. 23 (2014), 727-764
DOI: https://doi.org/10.1090/S1056-3911-2014-00636-6
Published electronically: March 3, 2014
MathSciNet review: 3263667
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Abstract | References | Additional Information

Abstract: We discuss geometric invariant theory (GIT) for canonically embedded genus $4$ curves and the connection to the Hassett–Keel program. A canonical genus $4$ curve is a complete intersection of a quadric and a cubic, and, in contrast to the genus $3$ case, there is a family of GIT quotients that depend on a choice of linearization. We discuss the corresponding variation of GIT (VGIT) problem and show that the resulting spaces give the final steps in the Hassett–Keel program for genus $4$ curves.

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Additional Information

Sebastian Casalaina-Martin
Affiliation: University of Colorado, Department of Mathematics, Boulder, Colorado
MR Author ID: 754836
Email: casa@math.colorado.edu

David Jensen
Affiliation: Stony Brook University, Department of Mathematics, Stony Brook, New York
Email: djensen@math.sunysb.edu

Radu Laza
Affiliation: Stony Brook University, Department of Mathematics, Stony Brook, New York
MR Author ID: 692317
ORCID: 0000-0001-9631-1361
Email: rlaza@math.sunysb.edu

Received by editor(s): March 22, 2012
Received by editor(s) in revised form: August 6, 2012, November 5, 2012, and November 16, 2012
Published electronically: March 3, 2014
Additional Notes: The first author was partially supported by NSF grant DMS-1101333
The third author was partially supported by NSF grant DMS-0968968 and a Sloan Fellowship
Article copyright: © Copyright 2014 University Press, Inc.