Related papers: Todd genera of complex torus manifolds

Assume that $M$ is a compact connected unitary 2n-dimensional manifold and admits a non-trivial circle action preserving the given complex structure. If the first Chern class of $M$ equals to $k_0x$ for a certain 2nd integral cohomology…

In 2006 Masuda and Suh asked if two compact non-singular toric varieties having isomorphic cohomology rings are homeomorphic. In the first part of this paper we discuss this question for topological generalizations of toric varieties,…

We show that a compact Kaehler manifold X is a complex torus if both the continuous part and discrete part of some automorphism group G of X are infinite groups, unless X is bimeromorphic to a non-trivial G-equivariant fibration. Some…

We write the equivariant Todd class of a general complete toric variety as an explicit combination of the orbit closures, the coefficients being analytic functions on the Lie algebra of the torus which satisfy Danilov's requirement.

We show that if a holomorphic $n$ dimensional compact torus action on a compact connected complex manifold of complex dimension $n$ has a fixed point then the manifold is equivariantly biholomorphic to a smooth toric variety.

A cohomology class u of a topological space X is atoroidal if its pullback to the torus vanishes for every map from a torus to X. Furthermore, X is atoroidally symplectic if there is an atoroidal cohomology class $u\in H^2(X;F)$ such that…

The equivariant cohomology of a space with a group action is not only a ring but also an algebra over the cohomology ring of the classifying space of the acting group. We prove that toric manifolds (i.e. compact smooth toric varieties) are…

This paper shows that the integral equivariant cohomology Chern numbers completely determine the equivariant geometric unitary bordism classes of closed unitary $G$-manifolds, which gives an affirmative answer to the conjecture posed by…

A toric manifold is a compact non-singular toric variety equipped with a natural half-dimensional compact torus action. A torus manifold is an oriented, closed, smooth manifold of dimension $2n$ with an effective action of a compact torus…

Let $M$ be a compact complex manifold. In this paper we give a simple proof of the bimeromorphic invariance of the higher Todd genera of $M$, a result first proved implicitly by Brasselet-Sch\"urmann-Yokura using algebraic methods.

The aim of this paper is to classify simply connected 6-dimensional torus manifolds with vanishing odd degree cohomology. It is shown that there is a one-to-one correspondence between equivariant diffeomorphism types of these manifolds and…

A quasitoric manifold is a smooth 2n-manifold M^{2n} with an action of the compact torus T^n such that the action is locally isomorphic to the standard action of T^n on C^n and the orbit space is diffeomorphic, as manifold with corners, to…

Let G be a group of automorphisms of a compact K\"ahler manifold X of dimension n and N(G) the subset of null-entropy elements. Suppose G admits no non-abelian free subgroup. Improving the known Tits alternative, we obtain that, up to…

We introduce the category of {\it locally $k$-standard $T$-manifolds} which includes well-known classes of manifolds such as toric and quasitoric manifolds, good contact toric manifolds and moment-angle manifolds. They are smooth manifolds…

We restrict geometric tangential equivariant complex $T^n$-bordism to torus manifolds and provide a complete combinatorial description of the appropriate non-commutative ring. We discover, using equivariant $K$-theory characteristic…

Let $Q$ be a compact, connected $n$-dimensional Riemannian manifold, and assume that the geodesic flow is toric integrable. If $n \neq 3$ is odd, or if $\pi_1(Q)$ is infinite, we show that the cosphere bundle of $Q$ is equivariantly…

We study torsion in the integral cohomology of a certain family of $2n$-dimensional orbifolds $X$ with actions of the $n$-dimensional compact torus. Compact simplicial toric varieties are in our family. For a prime number $p$, we find a…

A basic problem in the classification theory of compact complex manifolds is to give simple characterizations of complex tori. It is well known that a compact K\"ahler manifold $X$ homotopically equivalent to a a complex torus is…

Topologically, compact toric varieties can be constructed as identification spaces: they are quotients of the product of a compact torus and the order complex of the fan. We give a detailed proof of this fact, extend it to the non-compact…

It is conjectured that to test the K-polystability of a polarised variety it is enough to consider test-configurations which are equivariant with respect to a torus in the automorphism group. We prove partial results towards this…