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논문 기본 정보
- 자료유형
- 학위논문
- 저자정보
- 발행연도
- 2013
- 저작권
- 서강대학교 논문은 저작권에 의해 보호받습니다.
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Let $S$ be a minimal surface of general type with $p_g=0$ having an involution $\sigma$ over the field of complex numbers. It is well known that if the bicanonical map $\varphi_{|2K_{S}|}$ of $S$ is composed with $\sigma$ (i.e.\ $\varphi_{|2K_{S}|}$ factors through $\sigma$) then the quotient $S/\sigma$ is rational or birational to an Enriques surface.
We prove that for $K_{S}^{2}=5,6,7,8$ and an involution $\sigma$ for which $\varphi_{|2K_{S}|}$ is composed with $\sigma$, the quotient $S/\sigma$ is rational. This result applies in part to surfaces $S$ with $K_{S}^{2}=5$ for which $\varphi_{|2K_{S}|}$ has degree $4$ and is composed with an involution $\sigma$.
Moreover when $\varphi_{|2K_{S}|}$ is not composed with $\sigma$ we give a list of the possible models of the quotient $S/\sigma$ and their branch divisors induced by $\sigma$. Surfaces $S$ with $K_{S}^{2}=7$ for which the quotient $S/\sigma$ is birational to an Enriques surface are treated in detail.
Also we list the examples available in the literature.
We prove that for $K_{S}^{2}=5,6,7,8$ and an involution $\sigma$ for which $\varphi_{|2K_{S}|}$ is composed with $\sigma$, the quotient $S/\sigma$ is rational. This result applies in part to surfaces $S$ with $K_{S}^{2}=5$ for which $\varphi_{|2K_{S}|}$ has degree $4$ and is composed with an involution $\sigma$.
Moreover when $\varphi_{|2K_{S}|}$ is not composed with $\sigma$ we give a list of the possible models of the quotient $S/\sigma$ and their branch divisors induced by $\sigma$. Surfaces $S$ with $K_{S}^{2}=7$ for which the quotient $S/\sigma$ is birational to an Enriques surface are treated in detail.
Also we list the examples available in the literature.
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