Compactified Deligne-Lusztig varieties with negative canonical divisors are identified in dimension two with the supersingular K3 surface of Artin invariant 1 in char 2 and ruled surfaces from supersingular elliptic curves or the Ree curve.
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Deligne-Lusztig varieties whose canonical divisors have negativity
Compactified Deligne-Lusztig varieties with negative canonical divisors are identified in dimension two with the supersingular K3 surface of Artin invariant 1 in char 2 and ruled surfaces from supersingular elliptic curves or the Ree curve.