10 papers
An almost Kähler Cheeger--Gromoll splitting theorem with applications
Anthony Nguyen, Shengzhen Ning, Lauren Pusey-Nazzaro
In this paper, we establish an almost Kähler analogue of the Cheeger--Gromoll splitting theorem for complete almost Kähler manifolds with nonnegative Ricci curvature. As applicatio…
The spaces of Kähler and holomorphically tamed symplectic forms on closed 4-manifolds
Tian-Jun Li, Shengzhen Ning
This paper investigates the uniqueness, connectedness and openness properties of spaces of Kähler forms on closed -manifolds, extending discussions in \cite{Li08,Sal13}. Motivat…
Symplectic log Kodaira dimension , Hirzebruch--Jung strings and weighted projective planes
Tian-Jun Li, Shengzhen Ning
We study symplectic minimal resolutions of weighted projective planes from the perspective of disconnected symplectic divisors with symplectic log Kodaira dime…
Equivariant Morse-Bott cohomology through stabilization
Erkao Bao, Robi Huq, Shengzhen Ning
For closed manifolds with compact Lie group actions, we study Austin-Braam's Morse-theoretic construction of Borel equivariant cohomology using the technique of stabilization. We s…
Cohomologous symplectic forms with different Gromov widths
Shengzhen Ning
We study McDuff-Salamon's Problem 46 by showing that there exist closed manifolds of dimension admitting cohomologous symplectic forms with different Gromov widths. The ex…
Symplectic log Kodaira dimension , affine-ruledness and unicuspidal rational curves
Tian-Jun Li, Shengzhen Ning
Given a closed symplectic -manifold , a collection of embedded symplectic submanifolds satisfying certain normal crossing conditions is called a symplectic divisor. I…
Comparing Kahler cone and symplectic cone of one-point blowup of Enriques surface
Shengzhen Ning
We follow the study by Cascini-Panov on symplectic generic complex structures on Kahler surfaces with , a question proposed by Tian-Jun Li, by demonstrating that the one-poi…
Algebraic capacities as tropical polynomials over the reduced -positive symplectic cone
Tian-Jun Li, Shengzhen Ning
In a series of work [Wor22], [Wor21] and [CW20], algebraic capacities were introduced in an algebraic manner for polarized algebraic surfaces and applied to the symplectic embeddin…
Almost toric presentations of symplectic log Calabi-Yau pairs
Tian-Jun Li, Jie Min, Shengzhen Ning
It is known that the union of fibers over elliptic singularities of an almost toric fibered (ATF) closed symplectic four-manifold forms a symplectic log Calabi-Yau (LCY) divisor. I…
Enumerative aspect of symplectic log Calabi-Yau divisors and almost toric fibrations
Tian-Jun Li, Jie Min, Shengzhen Ning
In this paper we are interested in the isotopy classes of symplectic log Calabi-Yau divisors in a fixed symplectic rational surface. We give several equivalent definitions and prov…