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A Proof of the Weierstraß Gap Theorem not Using the Riemann–Roch Formula
Usually, the Weierstraß gap theorem is derived as a straightforward corollary of the Riemann–Roch theorem. Our main objective in this article is to...
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Optimal constant in an L 2 extension problem and a proof of a conjecture of Ohsawa
In this paper, we solve the optimal constant problem in the setting of Ohsawa’s generalized L 2 extension theorem. As applications, we prove a...
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Special values of canonical Green’s functions
We give a precise formula for the value of the canonical Green’s function at a pair of Weierstrass points on a hyperelliptic Riemann surface. Further...
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On curves with all Weierstrass points of maximal weight
In this note we show that the few known examples of non-hyperelliptic complex algebraic curves all of whose Weierstrass points have maximal weight...
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Existence of the non-primitive Weierstrass gap sequences on curves of genus 8
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...
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Weierstrass semigroups whose minimum positive integers are even
We consider three subsets of the set of 2 n -semigroups, where for a positive integer n a 2 n -semigroup means a numerical semigroup whose minimum...
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The Weierstrass semigroup of a pair of GaloisWeierstrass points with prime degree on a curve
We describe the Weierstrass semigroup of a Galois Weierstrass point with prime degree and the Weierstrass semigroup of a pair of Galois Weierstrass...
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Weierstrass Semigroups of a Pair of Points Whose First Nongaps are Three
We found all candidates for a Weierstrass semigroup at a pair of Weierstrass points whose first nongaps are three. We prove that such semigroups are...
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The Weierstrass semigroup of a pair and moduli in
M 3We classify all the Weierstrass semigroups of a pair of points on a curve of genus 3, by using its canonical model in the plane. Moreover, we count...
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Numerical semigroups which cannot be realized as semigroups of Galois Weierstrass points
Morrison and Pinkham [4] gave a characterization of the semigroups of Galois Weierstrass points , i.e., total ramification points of cyclic coverings...
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Non-Cyclic Weierstrass Semigroups
Morrison and Pinkham [5] gave a characterization of the semi-groups of Galois Weierstrass points, i.e., total ramification points of cyclic coverings...