Some degenerations of and Calabi–Yau varieties

  • Michał Kapustka

    Jagiellonian University, Krakow, Poland
Some degenerations of $G_2$ and Calabi–Yau varieties cover

A subscription is required to access this book chapter.


We introduce a variety parameterizing isotropic five-spaces of a general degenerate four-form in a seven dimensional vector space. It is in a natural way a degeneration of the variety , the adjoint variety of the simple Lie group . It occurs that it is also the image of by a system of quadrics containing a twisted cubic. Degenerations of this twisted cubic to three lines give rise to degenerations of which are toric Gorenstein Fano fivefolds. We use these two degenerations to construct geometric transitions between Calabi–Yau threefolds. We prove moreover that every polarized K3 surface of Picard number 2, genus 10, and admitting a appears as linear sections of the variety .