The moduli spaces of bielliptic curves of genus 4 with more bielliptic structures

• Autores: G. Casnati, Andrea Del Centina
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 71, Nº 3, 2005, págs. 599-621
• Idioma: inglés
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• Resumen

  • Let be an irreducible, smooth, projective curve of genus over the complex field . The curve is called if it admits a degree-two morphism onto an elliptic curve ; such a morphism is called a on . If is bielliptic and , then the bielliptic structure on is unique, but if , then this holds true only generically and there are curves carrying bielliptic structures. The sharp bounds exist for respectively. Let be the coarse moduli space of irreducible, smooth, projective curves of genus . Denote by the locus of points in representing curves carrying at least bielliptic structures. It is then natural to ask the following 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? Complete answers are given to the above questions in the case .