Hodge metrics and the curvature of higher direct images

By Christophe Mourougane, S. Takayama. 2007

56 citations recorded by the source corpus.

Using the harmonic theory developed by Takegoshi for representation of relative cohomology and the framework of computation of curvature of direct images bundles by Berndtsson, we prove that the higher direct images by a smooth morphism of the relative canonical bundle twisted by a semi-positive vector bundle are locally free and semi-positively curved, when endowed with a suitable Hodge type metric.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f83027749192e74b871ecf4d6d56891b84706fe1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Xiaokui Yang
2. Kefeng Liu
3. Mihai Puaun
4. Xiaofeng Sun
5. S. Takayama
6. Valentino Tosatti
7. Fang Zheng
8. Christopher D. Hacon

In Mathematical Physics

1. Mihai Puaun
2. Kefeng Liu
3. Xiaofeng Sun
4. S. Takayama
5. Xiaokui Yang
6. Christopher D. Hacon
7. J. McKernan

Citations in the corpus

• Positivity of twisted relative pluricanonical bundles and their direct images (2014, background): “Actually this field has generated many important works, including the twisted case by a semi-ample line bundle L; we will only mention here a few of them [1], [7], [18], [22], [24], [25], [26], [28], [29], [32], [33], [34], [47] (and we apologize to the authors we omit .”
• Positivity and vanishing theorems for ample vector bundles (2010, background): “For more related results, we refer the reader to [2], [3] [4], [27], [28] and [33] and references therein.”