HODGE THEORY AND COMPLEX ALGEBRAIC GEOMETRY, I (Cambridge Studies in Advanced Mathematics 76) By CLAIRE VOISIN: 322 pp., £55.00 (US$80.00), ISBN 0-521-80260-1 (Cambridge University Press, 2002).

TL;DR: In this paper, it was shown that for any natural number p, the sheaf (X, D) of reflexive logarithmic p-forms does not contain a Weil divisorial subsheaf whose Kodaira-Iitaka dimension exceeds p. The main ingredients to the proof are the extension theorem of Greb-Kebekus-Kov\'acs-Peternell, a new version of the Negativity lemma, the minimal model program, and a residue map for symmetric differentials on dlt pairs.

TL;DR: In this article, the existence of various harmonic maps from Hermitian manifolds to Kaehler, Hermitians, and Riemannian manifold was studied, and the complex analyticity of pluri-harmonic maps from compact complex manifolds with non-degenerate curvatures was obtained.

TL;DR: In this article, it was shown that there does not exist a crepant resolution of MJ(2,0,2n) for n ≥ 2, which is a singular projective variety, endowed with a holomorphic symplectic structure on the smooth locus.

TL;DR: In this paper, the authors associate objects in the Kuznetsov component of a Fano threefold $Y$ of index 2 and Picard rank 1 are del Pezzo surfaces, and their Picard group is related to a root system.