Extension of twisted Hodge metrics for Kähler morphisms
Extension of twisted Hodge metrics for Kähler morphisms
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Kähler 态射的扭曲 Hodge 度量的扩展
DOI：
10.4310/jdg/1253804353
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发表时间：
2008
影响因子：
2.5
通讯作者：
S. Takayama
中科院分区：
文献类型：
--
作者：
Christophe Mourougane;S. Takayama
设f：X->；Y是复流形的全纯映射，它是真的、Kahler的、有连通纤维的满射，且在Y-Z上光滑，是解析子集Z的补.设E是X上的Nakano半正向量丛，考虑Q0的直象层F=R^QF*(K_{X/Y}\oE).在前面的文章中，我们讨论了当映射f是光滑的时，F关于所谓的Hodge度量的Nakano半正性。本文讨论了射影空间丛P(F)“在Y-Z上”上的重言线丛O(1)上的诱导度量作为具有半正曲率“在Y上”的奇异Hermite度量的扩张。作为一个特殊的推论，如果Y是射影的，则R^QF*(K_{X/Y}×E)在Viehweg意义下弱正于Y-Z。
Let f : X --> Y be a holomorphic map of complex manifolds, which is proper, Kahler, and surjective with connected fibers, and which is smooth over Y-Z the complement of an analytic subset Z. Let E be a Nakano semi-positive vector bundle on X, and consider direct image sheaves F = R^qf_*(K_{X/Y} \otimes E) for q \geq 0. In our previous paper, we discussed the Nakano semi-positivity of F with respect to the so-called Hodge metric, when the map f is smooth. In this paper, we discuss the extension of the induced metric on the tautological line bundle O(1) on the projective space bundle P(F) ``over Y-Z'' as a singular Hermitian metric with semi-positive curvature ``over Y''. As a particular consequence, if Y is projective, R^qf_*(K_{X/Y} \otimes E) is weakly positive over Y-Z in the sense of Viehweg.