3 papers
math.CV2026
Hodge theory for twisted log-differential forms
Junyan Cao
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 Den…
math.AG2025
Hodge theory for local systems and cohomological support loci
Junyan Cao, Ya Deng, Christopher D. Hacon +1
In this article, we pursue two main objectives. The first is to show that the fundamental results of Green-Lazarsfeld (1987, 1991) on generic vanishing theorems, and works of Budur…
math.CV2025
Remarks on Relative Canonical Bundles and Algebraicity Criteria for Foliations in Kähler context
Junyan Cao, Mihai PÄun
In this note, motivated by the recent preprint of W. Ou, we pursue three main objectives. The first is to make progress towards the positivity of the relative canonical bundle in t…