Chow Rings, Decomposition of the Diagonal, and the Topology of Families
Chow Rings, Decomposition of the Diagonal, and the Topology of Families
复制标题
松狮环、对角线分解和族拓扑
DOI：
10.1515/9781400850532
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发表时间：
2014
影响因子：
3.1
通讯作者：
C. Voisin
中科院分区：
文献类型：
--
作者：
C. Voisin
序言vii 1引言1 1.1对角线的分解和扩展3 1.2广义Bloch猜想7 1.3小对角线的分解和对族拓扑的应用9 1.4整系数和双有理不变量11 1.5文本的组织13 2霍奇理论和代数圈的回顾15 2.1 Chow群15 2.2霍奇结构24 3对角线的分解36 3.1一般原理36 3.2具有小Chow群的变种44 4大Coniveau完全相交的Chow群55 4.1完全相交的Hodge Coniveau 55 4.2 Coniveau 2完全相交64 4.3一般完全相交的广义Bloch和Hodge拓扑的等价性67 4.4对关于曲面上0-圈的Bloch猜想86 5关于K3曲面的Chow环和超Chow环Kahler流形88 5.1 K3曲面的重言环88 5.2小对角线的分解96 5.3 K3曲面族的Deligne分解定理106 6积分系数123 6.1积分Hodge类和双有理不变量123 6.2理性连通簇和合理性问题127 6.3对角线的积分分解和Abel-Jacobi映射的结构139参考书目155索引163
Preface vii 1Introduction 1 1.1 Decomposition of the diagonal and spread 3 1.2 The generalized Bloch conjecture 7 1.3 Decomposition of the small diagonal and application to the topology of families 9 1.4 Integral coefficients and birational invariants 11 1.5 Organization of the text 13 2Review of Hodge theory and algebraic cycles 15 2.1 Chow groups 15 2.2 Hodge structures 24 3Decomposition of the diagonal 36 3.1 A general principle 36 3.2 Varieties with small Chow groups 44 4Chow groups of large coniveau complete intersections 55 4.1 Hodge coniveau of complete intersections 55 4.2 Coniveau 2 complete intersections 64 4.3 Equivalence of generalized Bloch and Hodge conjectures for general complete intersections 67 4.4 Further applications to the Bloch conjecture on 0-cycles on surfaces 86 5On the Chow ring of K3 surfaces and hyper-Kahler manifolds 88 5.1 Tautological ring of a K3 surface 88 5.2 A decomposition of the small diagonal 96 5.3 Deligne's decomposition theorem for families of K3 surfaces 106 6Integral coefficients 123 6.1 Integral Hodge classes and birational invariants 123 6.2 Rationally connected varieties and the rationality problem 127 6.3 Integral decomposition of the diagonal and the structure of the Abel-Jacobi map 139 Bibliography 155 Index 163