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Weierstrass points, inflection points and ramification points of curves
Ballico, Edoardo
1998
Abstract
Let C be an integral curve of the smooth projective surface S and
P $\epsilon$ C. Let $\pi:X\rightarrow C$ be the normalization and
$Q\epsilon X$ with $\pi\left(Q\right)=P$. We are interested in the
case in which Q is a Weierstrass point of X. We compute the semigroup
N(Q, X) of non-gaps of Q when S is a Hirzebruch surface $F_{e}P\epsilon C_{reg}$
and P is a total ramification point of the restriction to C of a ruling
$F_{e}\rightarrow P^{1}$. We study also families of pairs (X, Q)
such that the first two integers of N( Q, X) are k and d. To do that
we study families of pairs (P,C) with C plane curve, deg(C) =d, C
has multiplicity d - k at P, C is unibranch at P and a line through
P has intersection multiplicity d with C at P.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
30 (1998)
Publisher
Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Source
Edoardo Ballico, "Weierstrass points, inflection points and ramification points of curves", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 30 (1998), pp. 141-154.
Languages
en
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