Automorphisms of smooth canonically polarized surfaces in positive characteristic
Date
2017Source
Advances in MathematicsVolume
310Pages
235-289Google Scholar check
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This paper investigates the geometry of a smooth canonically polarized surface X defined over an algebraically closed field of characteristic p>0 in the case when the automorphism scheme of X is not smooth. In particular, it is shown that a smooth canonically polarized surface X with 1≤KX 2≤2 and non-smooth automorphism scheme tends to be uniruled and simply connected and is the purely inseparable quotient of a ruled or rational surface by a rational vector field. Moreover, restrictions on certain numerical invariants of X are obtained in order for Aut(X) to be smooth. © 2017 Elsevier Inc.