Jakub Jagiełła

University of Warsaw

Resolution of singularities of small secant varieties of Segre varieties

The geometry of secant varieties of Segre varieties is very complicated and poorly understood. However, we can say more about the open locus consisting of minimal border rank tensors. In terms of singularities, its local geometry is equivalent to the geometry of some well-studied moduli spaces, such as Hilbert schemes of points. We introduce concise secant varieties, which come with projective birational maps to the usual secant varieties. They are smoothly equivalent to the concise locus of usual secant varieties, meaning that their singularities are governed by the singularities of moduli spaces. We use this new setup, alongside known results about the geometry of moduli spaces, to construct resolutions of singularities of small secant varieties. This is a joint work with Joachim Jelisiejew.