Stability of genus five canonical curves

2013/02/20 by Maksym Fedorchuk, Fedorchuk, Maksym, David Ishii Smyth +1 · 1 citation
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1302.4804

openalex publication_date 2013/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We analyze GIT stability of nets of quadrics in ℙ⁴ up to projective equivalence. Since a general net of quadrics defines a canonically embedded smooth curve of genus five, the resulting GIT quotient gives a birational model of the moduli space of genus 5 curves. We study the geometry of the associated contraction and prove that the constructed GIT quotient is the final step of the log minimal model program for the moduli space of genus 5 curves.

Citations

• Log minimal model program for the moduli space of stable curves: The first flip

Cited by

• Mori's program for M_0,6 with symmetric divisors

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