The jumping phenomenon of Hodge numbers

Xuanming Ye

Vol. 235 (2008), No. 2, 379–398

DOI: 10.2140/pjm.2008.235.379

Abstract

Let X be a compact complex manifold, and let π : 𝒳 → B be a small deformation of X. The dimensions of the Dolbeault cohomology groups H^q(X_t,Ω_Xt^p) may vary under this deformation. In this paper, we will study the deformation obstructions of a (p,q)-class in the central fiber X. In particular, we obtain an explicit formula for the obstructions and apply this formula to the study of small deformations of the Iwasawa manifold.

Keywords

Hodge number, Deformation, Obstruction, Kodaira Spencer Class

Mathematical Subject Classification 2000

Primary: 20G10, 13D10, 32G05

Milestones

Received: 20 November 2007

Accepted: 10 January 2008

Published: 1 April 2008