$L^2$-Extension of Adjoint bundles and Koll\'ar's Conjecture

Junchao Shentu; Chen Zhao

$L^2$-Extension of Adjoint bundles and Koll\'ar's Conjecture

Algebraic Geometry 2021-06-28 v1

Authors: Junchao Shentu , Chen Zhao

Abstract

We give a new proof of Koll\'ar's conjecture on the pushforward of the dualizing sheaf twisted by a variation of Hodge structure. This conjecture was settled by M. Saito via mixed Hodge modules and has applications in the investigation of Albanese maps. Our technique is the $L^2$ -method and we give a concrete construction and proofs of the conjecture. The $L^2$ point of view allows us to generalize Koll\'ar's conjecture to the context of non-abelian Hodge theory.

Keywords

kollár's conjecture dualizing sheaf variation of hodge structure l2-method adjoint bundle non-abelian hodge theory

Cite

@article{arxiv.2106.13407,
  title  = {$L^2$-Extension of Adjoint bundles and Koll\'ar's Conjecture},
  author = {Junchao Shentu and Chen Zhao},
  journal= {arXiv preprint arXiv:2106.13407},
  year   = {2021}
}

Comments

28 pages. Comments are welcomed

$L^2$-Extension of Adjoint bundles and Koll\'ar's Conjecture

Abstract

Keywords

Cite

Comments

Related papers