3 papers
math.AG2026
Numerical Reduction and Sharp Thresholds for Adjoint Singularities of Foliated Surfaces
Shi Xu
Let \((X,\mathcal F)\) be a foliated surface over the complex numbers. We study the variation of \(ε\)-adjoint singularities associated with the adjoint divisor \[ K_{\mathcal F}+…
math.AG2026
Noether-type inequalities for big divisors via control of the negative part
Shi Xu
Let be a smooth projective surface over and a big divisor with Zariski decomposition . We study the relationship between the volume $\mathrm{vol}(D)=P^2…
math.AG2026
Canonical Models of Adjoint Foliated Structures on Surfaces
Jun Lu, Xiaohang Wu, Shi Xu
In this paper, we study adjoint foliated structures of the form on algebraic surfaces and their minimal and canonical models. We investigate the effective behav…