2012/02/20 by Tuyen Trung Truong, Truong, Tuyen Trung · 2 citations
Mathematics · #Algebraic Geometry and Number Theory #Geometry and complex manifolds #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1202.4224
Let π:X→ ℙ3 be a finite composition of blowups along smooth centers. We show that for "almost all" of such X, if f∈ Aut(X) then its first and second dynamical degrees are the same. We also construct many examples of finite blowups X→ ℙ3, whose automorphism group Aut(X) has only finitely many connected components. We also present a heuristic argument showing that for a "generic" compact Kähler manifold X of dimension ≥ 3, the automorphism group Aut(X) has only finitely many connected components.