科研之友
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摘要
Let (G) over bar = (G, omega) be a vertex-weighted graph, and let delta be a divisor class on G. Let r ((G) over bar)(delta) denote the (combinatorial) rank of delta. Caporaso has introduced the algebraic rank r((G) over bar)(alg) (delta) of delta by using nodal curves with dual graph (G) over bar. In this paper, when (G) over bar is hyper elliptic or of genus 3, we show that r((G) over bar)(alg) (delta) >= r((G) over bar)(delta) holds, generalizing our previous result. We also show that, with respect to the specialization map from a nonhyperelliptic curve of genus 3 to its reduction graph, any divisor on the graph lifts to a divisor on the curve of the same rank.
- 出版日期2016-4
