Xiaowei Wang

Hilbert–Mumford criterion for nodal curves

We prove by the Hilbert–Mumford criterion that a slope stable polarized weighted pointed nodal curve is Chow asymptotic stable. This generalizes the result of Caporaso on stability of polarized nodal curves and of Hassett on weighted pointed stable curves polarized by the weighted dualizing sheaves. It also solves a question raised by Mumford and Gieseker, to prove the Chow asymptotic stability of stable nodal curves by the Hilbert–Mumford criterion.

Nonexistence of asymptotic GIT compactification

We provide examples of families of (log) smooth canonically polarized varieties, including smooth weighted pointed curves and smooth hypersurfaces in

Canonical metrics on stable vector bundles

P^3

Balance point and Stability of Vector Bundles Over a Projective Manifold

with large degree such that the Chow semistable limits under distinct pluricanonical embeddings do not stabilize.