Let D be a very general curve of degree d = 2 l - e in P^2, with e = 0,1, and let X in P^2 be an integral curve of geometric genus g and degree m, X different from D, and let n: C → X be the normalization. Let f be the degree of the reduction modulo 2 of the divisor n^*(D) of C. In this paper we prove the inequality 4g + f > m(d − 8 + 2e) + 5. We compare this with similar inequalities due to Geng Xu and Xi Chen.
Ciliberto, C., Flamini, F., Zaidenberg, M. (2019). A remark on the intersection of plane curves. In E.M.S. P. Kuchment (a cura di), Functional Analysis and Geometry. Selim Krein Centennial (pp. 109-128). Providence : American Mathematical Society [10.1090/conm/733/14737].
A remark on the intersection of plane curves
CILIBERTO, CIROMembro del Collaboration Group
;FLAMINI, FLAMINIO
Membro del Collaboration Group
;
2019-08-08
Abstract
Let D be a very general curve of degree d = 2 l - e in P^2, with e = 0,1, and let X in P^2 be an integral curve of geometric genus g and degree m, X different from D, and let n: C → X be the normalization. Let f be the degree of the reduction modulo 2 of the divisor n^*(D) of C. In this paper we prove the inequality 4g + f > m(d − 8 + 2e) + 5. We compare this with similar inequalities due to Geng Xu and Xi Chen.| File | Dimensione | Formato | |
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