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摘要翻译：
本文给出了对合曲面的一些数值限制条件。用这些公式研究了具有对合的曲面$S$,且$P_g=q=1$,使得$S/I$是非直纹曲面，并且$S$的双锥映射不是由$I构成的。给出了一个完整的可能性列表，并构造了几个新的例子，作为曲面的二重覆盖。特别地，给出了具有双元双锥映射的$P_g=q=1$和$K^2=7$的一般型极小曲面的第一个例子。
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英文标题：
《Involutions on surfaces with $p_g=q=1$》
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作者：
Carlos Rito
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
In this paper some numerical restrictions for surfaces with an involution are obtained. These formulas are used to study surfaces of general type $S$ with $p_g=q=1$ having an involution $i$ such that $S/i$ is a non-ruled surface and such that the bicanonical map of $S$ is not composed with $i.$ A complete list of possibilities is given and several new examples are constructed, as bidouble covers of surfaces. In particular the first example of a minimal surface of general type with $p_g=q=1$ and $K^2=7$ having birational bicanonical map is obtained.
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PDF链接：
https://arxiv.org/pdf/0805.4513
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