Chern numbers of Chern submanifolds

Topology of Blow-ups and Enumerative Geometry

Let M be the blow--up of a manifold M along a submanifold X. In this paper we present closed formulae for the integral cohomology and the total Chern class of M. As applications we compute the cohomology of the varieties of complete conics and complete quadrices in 3--space, and justify two enumerative results due to Schubert.

Homological stability for moduli spaces of disconnected submanifolds, I

A well-known property of unordered configuration spaces of points (in an open, connected manifold) is that their homology stabilises as the number of points increases. We generalise this result to moduli spaces of submanifolds of higher dimension, where stability is with respect to the number of components having a fixed diffeomorphism type and isotopy class. As well as for unparametrised submanifolds, we prove this also for partially-parametrised submanifolds -- where a partial parametrisation may be thought of as a superposition of parametrisations related by a fixed subgroup of the mapping …

Chern numbers of manifolds with torus action

We show that every set of numbers that occurs as the set of Chern numbers of an almost complex manifold $M^{2n}$, $n\geqslant 3$, may be realized as the set of Chern numbers of a connected almost complex manifold with an almost complex action of two-dimensional compact torus.

关于复双曲分支覆盖的Chern数比值

On ratios of Chern numbers for complex hyperbolic branched covers

本文证明偶数维复双曲分支覆盖流形的Chern数比值不同于复双曲流形，从而回答Deraux-Seshadri问题，并表明先前构造的几乎1/4-pinched度量非Kähler。