On the rank of quadratic equations for curves of high degree

2022/02/02 by Park, Euisung · 1 citation
#14C20 #14H99 #14N05 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2202.00857

Abstract

Let C ⊂ ℙ^r be a linearly normal curve of arithmetic genus g and degree d. In \citeSD, B. Saint-Donat proved that the homogeneous ideal I(C) of C is generated by quadratic equations of rank at most 4 whenever d ≥ 2g+2. Also, in \citeEKS Eisenbud, Koh and Stillman proved that I(C) admits a determinantal presentation if d ≥ 4g+2. In this paper, we will show that I(C) can be generated by quadratic equations of rank 3 if either g=0,1 and d ≥ 2g+2 or else g ≥ 2 and d ≥ 4g+4.

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