Stability of nets of quadrics in ℙ⁵ and associated discriminants

2015/02/27 by Byun, Sangho
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1502.07819

Abstract

Let S be a complete intersection surface defined by a net Λ of quadrics in \mathbb P⁵. In this paper we analyze GIT stability of nets of quadrics in \mathbb P⁵ up to projective equivalence, and discuss some connections between a net of quadrics and the associated discriminant sextic curve. In particular, we prove that if S is normal and the discriminant Δ(S) of S is stable then Λ is stable. And we prove that if S has the reduced discriminant and Δ(S) is stable then Λ is stable. Moreover, we prove that if S has simple singularities then Δ(S) has simple singularities.

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