Chow Stability of Canonical Genus 4 Curves

Kim, Ho‐Sung

doi:10.4134/bkms.2013.50.3.1029

Cited by 2 publications

(3 citation statements)

References 14 publications

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“…We note that our stability computation agrees with the partial analysis of Kim [Kim08] (who makes a direct computation of the stability conditions on Chow 4,1 ).…”

Section: Stability For Canonical Genus 4 Curvessupporting

confidence: 84%

“…is in fact the GIT quotient of the Chow variety Chow 4,1 associated to canonical curves in P 3 . We note that partial results on Chow 4,1 / / SL(4) were obtained by H. Kim [Kim08].…”

Section: Proposition 25 Pulling Back Sections Via the Rational Mapmentioning

confidence: 75%

“…We note that a partial analysis of the GIT on Chow 4,1 was done by H. Kim [Kim08] (motivated by the Hassett-Keel program). The approach of [Kim08] is to directly compute GIT stability conditions for Chow varieties (vs. our approach via cubic threefolds); our results agree with those of Kim. However, to our knowledge, Theorem 3.1 is the first complete analysis for GIT stability on Chow 4,1 , and also the first description of the Hassett-Keel space M 4 5 9 .…”

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confidence: 99%

See 2 more Smart Citations

The geometry of the ball quotient model of the moduli space of genus four curves

Casalaina-Martin¹,

Jensen²,

Laza³

2012

Compact Moduli Spaces and Vector Bundles

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Abstract. S. Kondo has constructed a ball quotient compactification for the moduli space of non-hyperelliptic genus four curves. In this paper, we show that this space essentially coincides with a GIT quotient of the Chow variety of canonically embedded genus four curves. More specifically, we give an explicit description of this GIT quotient, and show that the birational map from this space to Kondo's space is resolved by the blow-up of a single point. This provides a modular interpretation of the points in the boundary of Kondo's space. Connections with the slope nine space in the Hassett-Keel program are also discussed.

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