268,092 research outputs found
Compact K\"ahler manifolds with automorphism groups of maximal rank
For an automorphism group G on an n-dimensional (n > 2) normal projective
variety or a compact K\"ahler manifold X so that G modulo its subgroup N(G) of
null entropy elements is an abelian group of maximal rank n-1, we show that
N(G) is virtually contained in Aut_0(X), the X is a quotient of a complex torus
T and G is mostly descended from the symmetries on the torus T, provided that
both X and the pair (X, G) are minimal.Comment: Added Hypothesis (C) to Theorem 1.2. No change of the proof
Automorphism groups and anti-pluricanonical curves
We show the existence of an anti-pluricanonical curve on every smooth
projective rational surface X which has an infinite group G of automorphisms of
either null entropy or of type Z . Z (semi-direct product), provided that the
pair (X, G) is minimal. This was conjectured by Curtis T. McMullen (2005) and
further traced back to Marat Gizatullin and Brian Harbourne (1987). We also
prove (perhaps) the strongest form of the famous Tits alternative theorem.Comment: Mathematical Research Letters (to appear); 20 page
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