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Session

AG3: Algebraic Geometry Location: A701 Session Chair: Mateusz Michalek Session Chair: Botong Wang

Presentation 1

Compactifications of pencils of matrices into Grassmannians and their invariants Vincenzo Galgano1, Fulvio Gesmundo2, Hanieh Keneshlou3 1: MPI-CBG Dresden, Germany; 2: University of Toulouse, France; 3: Universität Würzburg, Germany Inspired by Schubert varieties, given a two-dimensional linear subspace of $n \times n$ matrices $L$, we study the geometry of its compactification $Y_L$ in the Grassmannian $\Gr(n,2n)$. We determine degree and singular locus of the surface $Y_L$, and show that the algebraic invariants of $L$ under $\GL(2)\times \GL(n) \times \GL(n)$ correspond to intersection numbers of special divisors in $Y_L$. This is an ongoing work with F. Gesmundo and H. Keneshlou.