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SMOOTH RATIONAL DEFORMATIONS OF SINGULAR CONTRACTIONS OF CLASS VII SURFACES

Banff International Research Station for Mathematical Innovation and Discovery

We consider normal compact surfaces $Y$ obtained from a minimal class VII surface $X$ by contraction of a cycle $C$ of $r$ rational curves with $c_2<0$. Our main result states that, if the obtained cusp is smoothable, then $Y$ is globally smoothable. The proof is based on a vanishing theorem for $H^2(Y,\Theta)$ where $\Theta$ is the dual the sheaf of K\"ahler forms. If $r\le b_2(X)$ any smooth small deformation of $Y$ is rational, and if $r=b_2(X)$ (i.e. when $X$ is a half-Inoue surface) any smooth small deformation of $Y$ is an Enriques surface.

Mathematics; Differential geometry; Algebraic geometry

video/mp4

Author affiliation: Aix-Marseille University

2020-04-26

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/74170

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/