Deformations of exceptional Weierstrass points

Diaz, Steven

doi:10.1090/S0002-9939-1986-0813798-8

Deformations of exceptional Weierstrass points
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Proc. Amer. Math. Soc. 96 (1986), 7-10 Request permission

Abstract:

Using first order deformation theory of pointed curves we show that the semigroup of a generic Weierstrass point whose semigroup has first nonzero element $k$ consists only of multiples of $k$ until after its greatest gap value, and that on the moduli space of curves two components of the divisor of points corresponding to curves possessing exceptional Weierstrass points intersect nontransversely.

References

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Enrico Arbarello, Weierstrass points and moduli of curves, Compositio Math. 29 (1974), 325–342. MR 360601
Steven Diaz, Tangent spaces in moduli via deformations with applications to Weierstrass points, Duke Math. J. 51 (1984), no. 4, 905–922. MR 771387, DOI 10.1215/S0012-7094-84-05140-8

Limit linear series, the irrationality of

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