The Kodaira dimension of the moduli of K3 surfaces

The moduli space of polarised K3 surfaces of degree 2d is a quasi-projective variety of dimension 19. For general d very little has been known about the Kodaira dimension of these varieties. In this paper we present an almost complete solution to this problem. Our main result says that this moduli space is of general type for d>61 and for d=46,50,54,58,60.Comment: 47 page

Numerical properties of isotrivial fibrations

In this paper we investigate the numerical properties of relatively minimal isotrivial fibrations \varphi \colon X \lr C, where $X$ is a smooth, projective surface and $C$ is a curve. In particular we prove that, if $g(C) \geq 1$ and $X$ is neither ruled nor isomorphic to a quasi-bundle, then K_X^2 \leq 8 \chi(\mO_X)-2; this inequality is sharp and if equality holds then $X$ is a minimal surface of general type whose canonical model has precisely two ordinary double points as singularities. Under the further assumption that $K_X$ is ample, we obtain K_X^2 \leq 8 \chi(\mO_X)-5 and the inequality is also sharp. This improves previous results of Serrano and Tan.Comment: 30 pages. Final version, to appear in Geometriae Dedicat

Respiratory failure due to tracheobronchomalacia.

A case is described of tracheobronchomegaly progressing to extensive tracheomalacia, complicated by episodic choking, recurrent pulmonary infections, and irreversible hypercapnic respiratory failure. A Y-shaped tracheobronchial stent was placed endoscopically to splint the trachea open, with excellent clinical and physiological improvement. New stent designs may provide long term palliation in selected cases of diffuse tracheal collapse or stenosis, and offer an alternative to surgical repair

Advanced module for model parameter extraction using global optimization and sensitivity analysis for electron-beam proximity effect correction

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