On the projective normality of double coverings over a rational surface

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• 作者：Biswajit Rajaguru ^{biswajit.rajaguru@ku.edu" class="auth_mail" title="E-mail the corresponding author} ; Lei Song ; ^{lsong@ku.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Projective normality ; Double covering ; Adjoint divisor
• 刊名：Journal of Algebra
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：469
• 期：Complete
• 页码：251-266
• 全文大小：411 K

文摘

We study the projective normality of a minimal surface X which is a ramified double covering over a rational surface S   with c802fb36fd1a0f" title="Click to view the MathML source">dim⁡|−K_S|≥1$\dim |-K_S|\ge 1$. In particular Horikawa surfaces, the minimal surfaces of general type with 53c8e2d">$K_X^2=2p_g(X)-4$, are of this type, up to resolution of singularities. Let π be the covering map from X to S  . We show that the Z₂${\mathbb{Z}}_2$-invariant adjoint divisors K_X+rπ^⁎A$K_X+r{\pi }^{⁎}A$ are normally generated, where the integer r≥3$r\ge 3$ and A is an ample divisor on S.