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Seminar of Algebraic Geometry in East Asia
 
9:00 - 10:00, April 16, 2021 (Friday)
broadcast in Room 515, Cosmology Bldg., Online seminar
(線上演講 於宇宙學大樓515教室收播)
On the Irrationality of Moduli Spaces of K3 Surfaces
Kuan-Wen Lai (University of Massachusetts, Amherst)

Abstract:

As for 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 work, we estimate how the irrationality grows with g in terms of the measure introduced by Moh and Heinzer. We proved that the growth is bounded by a polynomial in g of degree 15 and, for three sets of infinitely many genera, the bounds can be refined to polynomials of degree 10. These results are built upon the modularity of the generating series of these moduli spaces in certain ambient spaces, and also built upon the existence of Hodge theoretically associated cubic fourfolds, Gushel–Mukai fourfolds, and hyperkähler fourfolds. This is a collaboration with Daniele Agostini and Ignacio Barros (arXiv:2011.11025).
 
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