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Base point free pencils of small degree on certain smooth curves |
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| Authors: | AHW Schmitt |
| Institution: | (1) Department of Mathematics Education, Yeungnam University, 214-1 Daedong Gyeongsan, 712-749 Gyeongsangbuk-do, South Korea;(2) Department of Digital Broadcasting and Electronics Engineering, Chungwoon University, Chungnam, 350-701, South Korea;(3) Graduate School of Education, Hankuk University of Foreign Studies, 130-791 Seoul, South Korea;(4) Division of Foundational Mathematics, National Institute for Mathematical Sciences, 305-340 Daejeon, South Korea; |
| Abstract: | We give sufficient conditions on numbers d and m such that a linear system of degree m on the normalization C of a plane curve `(C)]\overline {C} of degree d which is in a certain sense not too singular is in the natural way induced by either a pencil of lines or a pencil of conics in the plane. Those results generalize results on nodal and cuspidal plane curves and seem to complement the recent results of 2]. We present a new approach via the geometry of curves in \Bbb P1×\Bbb P2{\Bbb P}_1\times {\Bbb P}_2. |
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