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math.AG2021
Complete curves in the moduli space of polarized K3 surfaces and hyper-Kähler manifolds
Olivier Debarre, Emanuele Macrì
Building on an idea of Borcherds, Katzarkov, Pantev, and Shepherd-Barron (who treated the case ), we prove that the moduli space of polarized K3 surfaces of degree conta…
math.AG2021
Gushel-Mukai varieties with many symmetries and an explicit irrational Gushel-Mukai threefold
Olivier Debarre, Giovanni Mongardi
We construct an explicit complex smooth Fano threefold with Picard number 1, index 1, and degree 10 (also known as a Gushel-Mukai threefold) and prove that it is not rational by sh…