A note on higher Todd genera of complex manifolds

Almost complex torus manifolds -- graphs, Hirzebruch genera, and problem of Petrie type

Let a $k$-dimensional torus $T^k$ act on a $2n$-dimensional compact connected almost complex manifold $M$ with isolated fixed points. As for circle actions, we show that there exists a (directed labeled) multigraph that encodes weights at the fixed points of $M$. This includes the notion of a GKM graph as a special case that weights at each fixed point are pairwise linearly independent. If in addition $k=n$, i.e., $M$ is an almost complex torus manifold, the multigraph is a graph; it has no multiple edges. We show that the Hirzebruch $χ_y$-genus $χ_y(M)=\sum_{i=0}^n a_i(M) \cdot (-y)^i$ of an …

复亏格、对称函数与多重 zeta 值

The complex genera, symmetric functions and multiple zeta values

本文研究复亏格的 Chern 数系数及其几何应用，并用统一框架处理多重 zeta 值公式与对称函数基转移矩阵。

A note on submanifolds of generalized Kähler manifolds

In this note, we consider submanifolds of a generalized Kähler manifold that are CR-submanifolds for the two associated Hermitian structures. Then, we establish the conditions for the induced, generalized F structure to be a CRFK structure. The results extend similar conditions which we obtained for hypersurfaces in an earlier paper.

A note on generalized laplacians and minimal surfaces

In these notes we give an interdisciplinary result which links the geometric concept of minimal surfaces with generalized harmonic functions.

Determinat Bundles and Geometric Quantization Of Vortex Moduli Spaces ON Compact Kahler Surfaces

In this paper we first show that on projective manifolds (M, ω), there are holomorphic determinant bundles (in the sense of Knusden-Mumford used by Bismut, Gillet, Soule) which play the role of the geometric quantum bundle, namely one for each input data of a Hermitian holomorphic line bundle L of non-trivial Chern class on a compact Kahler manifold Z (with Todd genus non-zero) and a choice of a geometric quantization of (M, ω). Next we further study the generalization of the vortex equations on Kahler 4-manifold which has been studied earlier by Bradlow. We show that when the Kahler 4-manifol…