On the modular curve X (6) and surfaces admitting genus 2 fibrations

ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

In this paper, we study the moduli spaces of surfaces admitting nonsmooth genus 2 fibrations with slope $lambda$ = 6 (necessarily) over curves of genus $geq$ 1. We determine the structure of each connected component of these moduli spaces. Our results fill the gap of earlier work in the literature to complete the picture of the moduli spaces of genus 2 fibrations over curves of genus $geq$ 2 except for the case of $lambda$ = 4.

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[1] Namba, M.: Families of Holomorphic Maps on Compact Riemann Surfaces, LNM767, Springer-Verlag (1979).
[2] Namba, M.: On nite galois coverings of projective manifolds, J. Math. Soc.Japan, 41(3), 391-403 (1989).
[3] Önsiper, H.: On moduli spaces of ber bundles of curves of genus 2, Arch. Math. 47(5), 346-348 (2000).
[4] Önsiper, H., Tekinel, C.: On the moduli of surfaces admitting genus 2 brations, to appear in Arch. Math.
[5] Seiler, W.: Moduli spaces for special surfaces of general type, in Algebraic Geometry and Its Applications (Ed: Bajaj), Springer-Verlag, 161-172 (1994).
[6] Seiler, W.: Moduli of surfaces of general type with a bration of genus 2 curves, Math.Ann., 301, 771-812 (1995).
[7] Shimura, G.: Introduction to the Arithmetic Theory of Automorphic Functions, PUP (1971).
[8] Xiao, G.: Surfaces Fibrees en Courbes de Genre Deux, LNM 1137, Springer-Verlag (1985).