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تسجيل مستخدم جديدSmooth Fano intrinsic Grassmannians of type $(2,n)$ with Picard number two
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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 Plucker 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 Fujitas freeness conjecture.
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