arXiv subjects

Wangyang Lin

Publications and source records attributed to Wangyang Lin.

3 recordsLinked to original sources

arXiv2026

Torsion algebras of Hermitian manifolds and rigidity

We regard the Chern torsion of a Hermitian manifold as a skew-symmetric complex-bilinear product on its holomorphic tangent bundle. For a compact connected Chern--K\"{a}hler-like Hermitian manifold, we prove that this product satisfies the Jacobi identity pointwise. If, in addition, the Chern holomorphic sectional curvature is strongly quasi-positive, we show that the resulting torsion Lie algebra is nilpotent and must be abelian. Consequently, the metric is K\"{a}hler. The underlying complex manifold is therefore projective and rationally connected. For general Hermitian manifolds, we construct a metric with positive real bisectional curvature on a Hopf surface which is neither simply connected nor rationally connected.

math.DG↗

arXiv2026

Inequalities for Chow Polynomials and Chern Numbers of Matroids

The Chow polynomial of a matroid is a fundamental invariant whose coefficients exhibit strong positivity properties, including $\gamma$-positivity. We interpret the normalized Chow coefficients as a probability distribution and establish new inequalities for its central moments. As consequences, we obtain bounds on the number of flags of flats and inequalities on the roots of the Chow polynomial. We further relate these moment inequalities to algebraic geometry via the Hirzebruch $\chi_y$-genus. This yields new inequalities for matroidal Chern numbers. In particular, for any matroid of rank $d+1$, we prove that $c_1c_{d-1}\le c_d$, with equality if and only if $d=1$ or the simplification of the matroid is Boolean.

math.CO↗

arXiv2024

Explicit formulas for the Hattori-Stong theorem and applications

We employ combinatorial techniques to present an explicit formula for the coefficients in front of Chern classes involving in the Hattori-Stong integrability conditions. We also give an evenness condition for the signature of stably almost-complex manifolds in terms of Chern numbers. As an application, it can be showed that the signature of a $2n$-dimensional stably almost-complex manifold whose possibly nonzero Chern numbers being $c_n$ and $c_ic_{n-i}$ is even, which particularly rules out the existence of such structure on rational projective planes. Some other related results and remarks are also discussed in this article.

math.DG↗