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We classify complex projective varieties of dimension $2r geq 8$ swept out by a family of codimension two grassmannians of lines $mathbb{G}(1,r)$. They are either fibrations onto normal surfaces such that the general fibers are isomorphic to $G(1,r)$ or the grassmannian $mathbb{G}(1,r+1)$. The cases $r=2$ and $r=3$ are also considered in the more general context of varieties swept out by codimension two linear spaces or quadrics.
In this article, we present a massively parallel framework for computing tropicalizations of algebraic varieties which can make use of finite symmetries. We compute the tropical Grassmannian TGr$_0(3,8)$, and show that it refines the $15$-dimensional
Associated to the cohomology ring A of the complement X(A) of a hyperplane arrangement A in complex m-space are the resonance varieties R^k(A). The most studied of these is R^1(A), which is the union of the tangent cones at the origin to the characte
Let $X$ be an integral scheme of finite presentation over a field. Let $q$ be a singular closed point of $X$. We prove that there exists an open subset $V$ of $X$ containing $q$ such that $V$ admits a resolution, that is, there exists a smooth scheme
We provide a characterization of Symplectic Grassmannians in terms of their Varieties of Minimal Rational Tangents.
We complement our previous computation of the Chow-Witt rings of classifying spaces of special linear groups by an analogous computation for the general linear groups. This case involves discussion of non-trivial dualities. The computation proceeds a