Birational boundedness of some Calabi-Yau hypersurfaces

Abstract: It is well-known that complex projective K3 surfaces are connected by analytic deformations, but they are algebraically unbounded. Nevertheless, Reid, Iano-Fletcher and Kollar-Johnson showed the finiteness of weighted Calabi-Yau hypersurfaces. Motivated by this, we study plt Calabi-Yau pairs (X,D) and show finiteness of D in some cases. In particular, we show that anticanonical K3 surfaces form a birationally bounded family. We also exhibit examples of K3 surfaces of a fixed degree whose birational contractions form an unbounded family, thus the birational boundedness is optimal in a sense.

algebraic geometry

Audience: researchers in the topic

ZAG (Zoom Algebraic Geometry) seminar

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