Building blocks of étale endomorphisms of complex projective manifolds

By Noboru Nakayama, De-Qi Zhang. 2009

67 citations recorded by the source corpus.

Étale endomorphisms of complex projective manifolds are constructed from two building blocks up to isomorphism if the good minimal model conjecture is true. They are the endomorphisms of abelian varieties and the nearly étale rational endomorphisms of weak Calabi–Yau varieties.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/f46d634421d2956288e3393458c04385df0fbf25

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In Geometry and Topology

Citations in the corpus

Polarized endomorphisms of complex normal varieties (2009, methodology): “We expect that dimS = 0 for the variety S in Theorem 1.1.”
Dynamics of automorphisms on projective complex manifolds (2008, background): “(d) See [42] Theorem B for a stonger result for the case of KX ≡ 0.”
Dynamics of automorphisms of compact complex surfaces (2014, background): “Hence, the image of Aut(X) in GL(H0(X ,K⊗n X ) ∗) is relatively compact and, in fact, is a finite group (see [121, 108]).”
ON THE DYNAMICAL DEGREES OF MEROMORPHIC MAPS PRESERVING A FIBRATION (2011, result): “Note that the same result was proved for compact Kähler surfaces by Cantat in [5] and Guedj in [15], for holomorphic maps on compact Kähler manifolds by Nakayama and Zhang in [17, 25], and for meromorphic maps on projective manifolds by the first and second authors in [8].”
Explicit Examples of rational and Calabi-Yau threefolds with primitive automorphisms of positive entropy (2013, unknown): “that λ 0(f|π) = 1, λk−l(f|π) is the topological degree of f|Xt as before and λp(f|π) ≥ 1 for any meaningful p. The following result was proved in [DNT11]. Some special cases were proved in [DN11] and [NZ09]. Theorem 3.2. Let f : X ··· → X , g : Y ··· → Y , π : X ··· → Y be dominant meromorphic maps ”