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Let S be a minimal surface of general type with pg(S) =q(S) = 0 having an involution σ over the field of complex numbers. It iswell known that if the bicanonical map φ of S is composed with σ, thenthe minimal resolution W of the quotient S/σ is rational or birational toan Enriques surface. In this paper we prove that the surface W of S withK2S = 5, 6, 7, 8 having an involution σ with which the bicanonical map φ of S is composed is rational. This result applies in part to surfaces S withK2S = 5 for which Ψ has degree 4 and is composed with an involution σ. Also we list the examples available in the literature for the given K2S andthe degree of φ.
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참고문헌 (31)
참고문헌 신청
A. Calabri / 2007 / Numerical Godeaux surfaces with an involution / Trans. Amer. Math. Soc 359 (4) : 1605 ~ 1632
A. Calabri / 2008 / Involutions on numerical Campedelli surfaces / Tohoku Math. J 60 (1) : 1 ~ 22
C. A. M. Peters / 1977 / On certain examples of surfaces with pg = 0 due to Burniat / Nagoya Math. J 66 : 109 ~ 119
C. Rito / / Some bidouble planes with pg = q = 0 and 4 K2 7 / math.AG/ arXiv:1103:2940
C. Rito / 2007 / On surfaces with pg = q = 1 and non-ruled bicanonial involution / Ann. Sc. Norm. Super. Pisa Cl. Sci 6 (1) : 81 ~ 102
A. Calabri / 2008 / Involutions on numerical Campedelli surfaces / Tohoku Math. J 60 (1) : 1 ~ 22
C. A. M. Peters / 1977 / On certain examples of surfaces with pg = 0 due to Burniat / Nagoya Math. J 66 : 109 ~ 119
C. Rito / / Some bidouble planes with pg = q = 0 and 4 K2 7 / math.AG/ arXiv:1103:2940
C. Rito / 2007 / On surfaces with pg = q = 1 and non-ruled bicanonial involution / Ann. Sc. Norm. Super. Pisa Cl. Sci 6 (1) : 81 ~ 102
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