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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 the result in [6] we see that every possible Weierstrass gap sequence of genus 8 is attained by some
pointed non-singular curve.
*Partially supported by Grant-in-Aid for Scientific Research (17540046), Japan Society for the Promotion of Science.
**Partially supported by Grant-in-Aid for Scientific Research (17540030), Japan Society for the Promotion of Science. 相似文献
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Jiryo Komeda 《manuscripta mathematica》1992,76(1):193-211
LetH be a numerical semigroup, i.e., a subsemigroup of the additive semigroup N of non-negative integers whose complement N/H in N is finite. Leta be the least positive integer inH. Then we show that ifa=5, then there exists a pointed complete non-singular irreducible algebraic curve (C, P) such thatH is the set of integers which are pole orders atP of regular functions onC/{P}. 相似文献
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Letters in Mathematical Physics - A recent generalization of the “Kleinian sigma function” involves the choice of a point P of a Riemann surface X, namely a “pointed curve”... 相似文献
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Jiryo Komeda 《Bulletin of the Brazilian Mathematical Society》1999,30(2):125-137
We show that for any possible Weierstrass gap sequenceL on a curve of genus 9 with twice the smallest positive non-gap > the largest gap there exists a pointed non-singular curve (C, P) over an algebraically closed field of characteristic 0 such that the gap sequence atP isL. 相似文献
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The authors determine all possible numerical semigroups at ramification points of double coverings of curves when the covered curve is of genus three and the covering curve is of genus eight. Moreover, it is shown that all of such numerical semigroups are actually of double covering type. 相似文献
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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 actually Weierstrass semigroups by constructing examples. 相似文献
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The zero divisor of the theta function of a compact Riemann surface X of genus g is the canonical theta divisor of Pic\({^{(g-1)}}\) up to translation by the Riemann constant \({\Delta}\) for a base point P of X. The complement of the Weierstrass gaps at the base point P gives a numerical semigroup, called the Weierstrass semigroup. It is classically known that the Riemann constant \({\Delta}\) is a half period, namely an element of \({\frac{1}{2}\Gamma_\tau}\) , for the Jacobi variety \({\mathcal{J}(X)=\mathbb{C}^{g}/\Gamma_\tau}\) of X if and only if the Weierstrass semigroup at P is symmetric. In this article, we analyze the non-symmetric case. Using a semi-canonical divisor D0, we express the relation between the Riemann constant \({\Delta}\) and a half period in the non-symmetric case. We point out an application to an algebraic expression for the Jacobi inversion problem. We also identify the semi-canonical divisor D0 for trigonal pointed curves, namely with total ramification at P. 相似文献
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