K3 surfaces with non-symplectic involution and compact irreducible G2-manifolds
K3 surfaces with non-symplectic involution and compact irreducible G2-manifolds
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具有非辛对合和紧致不可约 G2 流形的 K3 表面
DOI：
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发表时间：
2008
影响因子：
0.8
通讯作者：
Nam
中科院分区：
文献类型：
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作者：
A. Kovalev;Nam
本文考虑第一作者提出的构造具有完整性G2的紧致黎曼7-流形的连通和方法。该方法要求一对射影复形三重曲面具有反正则K3因子，且后者的K3曲面在其周期和Kähler类上必须满足一定的“匹配条件”。三重的合适的例子之前通过在Fano三重中吹出曲线而获得。本文利用Nikulin的非辛对合K3曲面理论，给出了一类新的代数三重曲面。这些三重性不能从上面的Fano三重性得到，并且允许匹配对导致拓扑上的新的紧致不可约G2-流形的例子。“地理”的贝蒂数b2，b3的新的（和以前已知的）例子的不可约G2流形的值进行了讨论。
Abstract We consider the connected-sum method of constructing compact Riemannian 7-manifolds with holonomy G2 developed by the first named author. The method requires pairs of projective complex threefolds endowed with anticanonical K3 divisors and the latter K3 surfaces should satisfy a certain ‘matching condition’ intertwining on their periods and Kähler classes. Suitable examples of threefolds were previously obtained by blowing up curves in Fano threefolds. In this paper, we give a large new class of 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 G2-manifolds. ‘Geography’ of the values of Betti numbers b2, b3 for the new (and previously known) examples of irreducible G2 manifolds is also discussed.