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arXiv · 2012.07155

Smooth Fano intrinsic Grassmannians of type $(2,n)$ with Picard number two

Muhammad Imran Qureshi·Milena Wrobel
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Abstract

We introduce the notion of intrinsic Grassmannians which generalizes the well known weighted Grassmannians. An intrinsic Grassmannian is a normal projective variety whose Cox ring is defined by the Pl\"ucker ideal $I_{d,n}$ of the Grassmannian $\mathrm{Gr}(d,n)$. We give a complete classification of all smooth Fano intrinsic Grassmannians of type $(2,n)$ with Picard number two and prove an explicit formula to compute the total number of such varieties for an arbitrary $n$. We study their geometry and show that they satisfy Fujita's freeness conjecture.

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Muhammad Imran Qureshi, Milena Wrobel. 2020-12-13. Smooth Fano intrinsic Grassmannians of type $(2,n)$ with Picard number two. https://arxiv.org/abs/2012.07155

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