Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 14 (2018), 055, 14 pages      arXiv:1608.08700      https://doi.org/10.3842/SIGMA.2018.055
Contribution to the Special Issue on Modular Forms and String Theory in honor of Noriko Yui

The Künneth Formula for the Twisted de Rham and Higgs Cohomologies

Kai-Chieh Chen a and Jeng-Daw Yu b
a) Department of Mathematics, University of California, Berkeley, Berkeley, CA, USA
b) Department of Mathematics, National Taiwan University, Taipei, Taiwan

Received February 23, 2018, in final form June 02, 2018; Published online June 12, 2018

Abstract
We prove the Künneth formula for the irregular Hodge filtrations on the exponentially twisted de Rham and the Higgs cohomologies of smooth quasi-projective complex varieties. The method involves a careful comparison of the underlying chain complexes under a certain elimination of indeterminacy.

Key words: de Rham complex; Hodge filtration; Künneth formula.

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