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Existence of the non-primitive Weierstrass gap sequences on curves of genus 8. (English) Zbl 1133.14307
Summary: We show that for any possible Weierstrass gap sequence \(L\) on a non-singular curve of genus 8 with twice the smallest positive non-gap is less than the largest gap there exists a pointed non-singular curve \((C, P)\) over an algebraically closed field of characteristic 0 such that the Weierstrass gap sequence at \(P\) is \(L\). Combining this with a result of the first author [J. Pure Appl. Algebra 97, No. 1, 51–71 (1994; Zbl 0849.14011)], we see that every possible Weierstrass gap sequence of genus 8 is attained by some pointed non-singular curve.

14H55 Riemann surfaces; Weierstrass points; gap sequences
14H30 Coverings of curves, fundamental group
14C20 Divisors, linear systems, invertible sheaves
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