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摘要翻译：
利用数学DG/0012189中发展的完整G2构造紧致黎曼7-流形的连通和方法。该方法要求具有反协调K3因子的射影复三元对，后者通过一定的非全纯映射“匹配”。在Math.DG/0012189中，通过在Fano三重法中炸毁曲线得到了三重法的合适例子。本文利用Nikulin的非辛对合K3曲面理论，进一步给出了合适的代数三重式。这三个是不能从上面的Fano三个中得到的，并且允许匹配对导致紧不可约G_2-流形的拓扑新例子。本文还讨论了紧不可约G_2流形的Betti数B^2,B^3值的地理分布。
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英文标题：
《K3 surfaces with non-symplectic involution and compact irreducible
G_2-manifolds》
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作者：
Alexei Kovalev and Nam-Hoon Lee
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最新提交年份：
2011
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分类信息：
一级分类：Mathematics 数学
二级分类：Differential Geometry 微分几何
分类描述：Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis
复形，接触，黎曼，伪黎曼和Finsler几何，相对论，规范理论，整体分析
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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：
We consider the connected-sum method of constructing compact Riemannian 7-manifolds with holonomy G_2 developed in math.DG/0012189. The method requires pairs of projective complex threefolds endowed with anticanonical K3 divisors, the latter `matching' via a certain non-holomorphic map. Suitable examples of threefolds were previously obtained in math.DG/0012189 by blowing up curves in Fano threefolds. In this paper, we give further suitable algebraic threefolds using theory of K3 surfaces with non-symplectic involution due to Nikulin. These threefolds are not obtainable from Fano threefolds, as above, and admit matching pairs leading to topologically new examples of compact irreducible G_2-manifolds. `Geography' of the values of Betti numbers b^2,b^3 for the new (and previously known) examples of compact irreducible G_2 manifolds is also discussed.
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PDF链接：
https://arxiv.org/pdf/0810.0957
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