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Specialization of dominant maps

Inder Kaur (Loughborough University)
Tuesday, March 28, 2023 - 1:30pm
PDL C-38
Title: Specialization of dominant maps
AbstractConsider a flat, projective family of geometrically integral varieties of relative dimension n over a discrete valuation ring. Suppose that there is a dominant rational map from the generic fiber to the projective n-space. In this talk I will give a sufficient criterion under which this dominant map extends (up to automorphism of P^n) to the entire family such that the restriction to the special fiber is again dominant. I will discuss how this fits with classical examples on rationality as well as applications to variation of irrationality. This is joint work in progress with Ananyo Dan.
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