The Moduli Spaces of Bielliptic Curves of Genus 4 with more Bielliptic Structures |
| |
Authors: | Casnati, G. Centina, A. Del |
| |
Affiliation: | Dipartimento di Matematica, Politecnico di Torino c.so Duca degli Abruzzi 24, 10129 Torino, Italy casnati{at}calvino.polito.it Dipartimento di Matematica, Università degli Studi di Ferrara via Machiavelli 35, 44100 Ferrara, Italy cen{at}dns.unife.it |
| |
Abstract: | Let C be an irreducible, smooth, projective curve of genus g 3 over the complex field C. The curve C is called biellipticif it admits a degree-two morphism : C E onto an ellipticcurve E such a morphism is called a bielliptic structure onC. If C is bielliptic and g6, then the bielliptic structureon C is unique, but if g=3,4,5, then this holds true only genericallyand there are curves carrying n>>1 bielliptic structures.The sharp bounds n 21,10,5 exist for g=3,4,5 respectively.Let Mg be the coarse moduli space of irreducible, smooth, projectivecurves of genus g=3,4,5. Denote by the locus of points in Mg $ representing curves carrying atleast n bielliptic structures. It is then natural to ask thefollowing questions. Clearly does hold? What are the irreducible components of ? Are the irreducible components of rational? How do the irreducible components of intersect each other? Let how many non-isomorphic elliptic quotients can it have? Completeanswers are given to the above questions in the case g=4. |
| |
Keywords: | |
本文献已被 Oxford 等数据库收录! |
|