Analytic Cycles and Vector Bundles on Non-Compact Algebraic Varieties.
Applications of the Kähler-Einstein-Calabi-Yau Metric to Moduli of K3 Surfaces.
Asymptotic behaviour of numerical invariants of algebraic varieties
We show that if the degree of a nonsingular projective variety is high enough, maximization of any of the most important numerical invariants, such as class, Betti number, and any of the Chern or middle Hodge numbers, leads to the same class of extremal varieties. Moreover, asymptotically (say, for varieties whose total Betti number is big enough) the ratio of any two of these invariants tends to a well-defined constant.