Compact Kähler manifolds with automorphism groups of maximal rank

Abstract

For an automorphism group $G$ on an $n$-dimensional ($n \ge 3$) normal projective variety or a compact Kähler 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 $\mathrm {Aut}_0(X)$, 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.

Locations

• arXiv (Cornell University) - View - PDF
• Transactions of the American Mathematical Society - View - PDF