Hodge theory for twisted log-differential forms
Junyan Cao
TL;DR
This survey reviews recent advances in extending Hodge theory to twisted log-differential forms with singular metrics, highlighting new theoretical frameworks and applications in complex geometry.
Contribution
It introduces new methods for Hodge theory in the context of singular metrics on bundles, expanding classical results to more general settings.
Findings
Development of Hodge theory for twisted log-differential forms
Extension of classical Hodge results to singular metrics
Applications to complex algebraic geometry
Abstract
In this survey, we review recent developments in extending Hodge theory to differential forms with values in bundles equipped with singular metrics, based on joint work with Ya Deng, Christopher D. Hacon, and Mihai P\u{a}un.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Homotopy and Cohomology in Algebraic Topology