Deformations of exceptional Weierstrass points

Author:
Steven Diaz

Journal:
Proc. Amer. Math. Soc. **96** (1986), 7-10

MSC:
Primary 14H15; Secondary 14F07, 32G15

DOI:
https://doi.org/10.1090/S0002-9939-1986-0813798-8

MathSciNet review:
813798

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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 consists only of multiples of 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.

**1.**Arbarello, E.**[1]***On subvarieties of the moduli space of curves of genus*defined in terms of Weierstrass points, Atti Accad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. Ia (8)**15**(1978), 3-20. MR**531917 (80f:14013)****[2]***Weierstrass points and moduli of curves*, Compositio Math.**29**(1974), 325-342. MR**0360601 (50:13048)****2.**Diaz, S.**[1]***Tangent spaces in moduli via deformations with applications to Weierstrass points*, Duke Math. J. (to appear). MR**771387 (86d:14023)****3.**Eisenbud D. and J. Harris**[1]***Limit linear series, the irrationality of*,*and other applications*, Bull. Amer. Math. Soc. (N.S.)**10**(1984), 277.**4.**Lax, R.F.**[1]***On the dimension of varieties of special divisors*, Trans. Amer. Math. Soc.**203**(1975), 141-159. MR**0360602 (50:13049)****[2]***Weierstrass points on the universal curve*, Math. Ann.**216**(1975), 35-42. MR**0384809 (52:5681)****5.**Rauch, H.**[1]***Weierstrass points, branch points, and moduli of Riemann surfaces*, Comm. Pure Appl. Math.**12**(1959), 543-560. MR**0110798 (22:1666)**

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DOI:
https://doi.org/10.1090/S0002-9939-1986-0813798-8

Article copyright:
© Copyright 1986
American Mathematical Society