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Title:
Estimates on the growth of irrationality for moduli spaces of K3 surfaces
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Abstract:
Similar to moduli spaces of curves, the moduli space of polarized K3 surfaces of genus g is of general type and thus is irrational for g sufficiently large. In this talk, I will introduce various estimates on how the irrationality grows with g in terms of the measure introduced by Moh and Heinzer. These estimates are built upon the modularity of the generating series of these moduli spaces in certain ambient spaces, as well as upon the existence of Hodge theoretically associated cubic fourfolds, Gushel–Mukai fourfolds, and hyperkähler fourfolds. This is joint work with Daniele Agostini and Ignacio Barros.
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