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The intersection of quadrics through a general curve of genus 4 and degree 9 in \({\mathbb{P}}^ 5\). (English) Zbl 0575.14006
By using Mumford’s theory [cf. D. Mumford, ”Varieties defined by quadratic equations” in: C.I.M.E. Varenna 1969, Quest. algebr. varieties, 29-100 (1970; Zbl 0198.258)], the author proves the following theorem: ”Let C be a nonhyperelliptic curve of genus 4, having two trigonal invertible sheaves and L an invertible sheaf of degree \(9(=2\cdot 4+1)\) on C. If \(h^ 0(L\otimes \omega_ C^{-1})=0\), then the homogeneous ideal defining \(\Phi_ L(C)\) \((=projective\) embedding of C) is generated by quadrics”.
Reviewer: E.Stagnaro
14C20 Divisors, linear systems, invertible sheaves
14H45 Special algebraic curves and curves of low genus
14M10 Complete intersections
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)