On the dynamical and arithmetic degrees of rational self-maps of algebraic varieties (40')
speaker: Joseph Silverman (Mathematics Department, Brown University)abstract: Let \(f : X \mapsto X\) be a dominant rational map of a projective variety defined over a number field. The (first) dynamical degree \(d(f)\) of \(f\) is the limit of the n'th root of the spectral radius of \((f^n)^*\) acting on \(NS(X)\). For an algebraic point \(P\) in \(X\) with well-defined forward orbit, the (upper) arithmetic degree \(a(f,P)\) is the lim sup of \(h_X(f^n(P))^{1/n}\), where \(h_X\) is a Weil height on X relative to an ample divisor. In this talk I will discuss the fundamental inequality \(a(f,P) \le d(f)\) and give an application to nef canonical heights. It is conjectured that \(a_f(P) = d_f\) whenever the orbit of \(P\) is Zariski dense; I will describe some cases for which we can prove this conjecture. (This is joint work with Shu Kawaguchi.)
timetable:
Tue 16 Oct, 15:30 - 16:10, Sala Conferenze Centro De Giorgi
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