Illinois Journal of Mathematics

On the Lefschetz and Hodge–Riemann theorems

Tien-Cuong Dinh and Viêt-Anh Nguyên

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We give an abstract version of the hard Lefschetz theorem, the Lefschetz decomposition and the Hodge–Riemann theorem for compact Kähler manifolds. Some examples are studied for compact symplectic Kähler manifolds.

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Illinois J. Math., Volume 57, Number 1 (2013), 121-144.

First available in Project Euclid: 23 June 2014

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Primary: 32Q15: Kähler manifolds 14C30: Transcendental methods, Hodge theory [See also 14D07, 32G20, 32J25, 32S35], Hodge conjecture 58A14: Hodge theory [See also 14C30, 14Fxx, 32J25, 32S35]


Dinh, Tien-Cuong; Nguyên, Viêt-Anh. On the Lefschetz and Hodge–Riemann theorems. Illinois J. Math. 57 (2013), no. 1, 121--144. doi:10.1215/ijm/1403534489.

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