WEIERSTRASS SEMIGROUPS AT PAIRS OF NON-WEIERSTRASS POINTS ON A SMOOTH PLANE CURVE OF DEGREE 5
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We classify all semigroups each of which arises as a Weierstrass semi- group at a pair of non-Weierstrass points on a smooth plane curve of degree 5. First we nd the candidates of semigroups by computing the dimensions of linear series on the curve. Then, by constructing examples of smooth plane curves of degree 5, we prove that each of the candidates is actually a Weierstrass semigroup at some pair of points on the curve. We need to study the systems of quadratic curves, which cut out the canonical series on the plane curve of degree 5.
Abstract
We classify all semigroups each of which arises as a Weierstrass semi- group at a pair of non-Weierstrass points on a smooth plane curve of degree 5. First we nd the candidates of semigroups by computing the dimensions of linear series on the curve. Then, by constructing examples of smooth plane curves of degree 5, we prove that each of the candidates is actually a Weierstrass semigroup at some pair of points on the curve. We need to study the systems of quadratic curves, which cut out the canonical series on the plane curve of degree 5.
참고문헌 (8)
- B. Brieskorn, "Plane Algebraic Curves. Modern Birkhauser Classics" (2012), Springer
- M. Coppens, "The existence of base point free linear systems on smooth plane curves", J. Algebraic Geometry, 4, pp.1~15 (1995)
- S. Greco, "The Luroth semigroup of plane algebraic curves", Pacific J. Math., 151, pp.43~56 (1991)
- M. Homma, "The Weierstrass semigroup of a pair of points on a curve", Arch. Math., 67, pp.337~348 (1996)
- S.J. Kim, "On the index of the Weierstrass semigroup of a pair of points on a curve", Arch. Math., 62, pp.73~82 (1994)
- S.J. Kim, "Weierstrass semigroups of pairs of points whose first non-gaps are three", Geometriae Dedicata, 93(1), pp.113~119 (2002)
- M. Namba, "Families of meromorphic functions on compact Riemann surfaces" (1979), Springer-Verlag
- J.G. Semple, "Introduction to Algebraic Geometry" (1985), Oxford University Press