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- W2140367066 abstract "We introduce a variety $hat{G}_2$ 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 $G_2$, the adjoint variety of the simple Lie group $mathbb{G}_2$. It occurs that it is also the image of $mathbb{P}^5$ by a system of quadrics containing a twisted cubic. Degenerations of this twisted cubic to three lines give rise to degenerations of $G_2$ 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 $g^1_5$ appears as linear sections of the variety $hat{G}_2$." @default.
- W2140367066 created "2016-06-24" @default.
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- W2140367066 date "2012-08-15" @default.
- W2140367066 modified "2023-09-27" @default.
- W2140367066 title "Some degenerations of $G_2$ and Calabi–Yau varieties" @default.
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