报告题目:Noether-Type Inequalities for Big Divisors via Control of the Negative Part

报告人: 徐识 (清华大学丘成桐数学中心 博士后)

报告时间：2026年7月17日（星期五）14：00

报告地点：数学科学学院114（小报告厅）

校内联系人：刘小雷 副教授 联系电话：84708351-8605

报告摘要: Let \(X\) be a smooth projective surface and let \(D\) be a big divisor with

Zariski decomposition \(D=P+N\). We study lower bounds for

\(\operatorname{vol}(D)=P^2\) in terms of \(h^0(X,D)\).

The main difficulty is the discrepancy between the Zariski decomposition

\(D=P+N\) and the linear system decomposition \(|D|=|M|+Z\). We introduce

a numerical invariant \(\mathfrak{C}(N)\), depending only on the negative part \(N\),

and use correction divisors supported on \(\operatorname{Supp}(N)\) to

compare the positive part \(P\) with the movable part \(M\).

Combining this numerical comparison with the geometry of the rational map

defined by \(|D|\), we obtain Noether-type inequalities and describe their

equality cases. The method applies in particular to adjoint divisors and

canonical divisors of relatively minimal foliations, for which \(\mathfrak{C}(N)\)

admits a uniform bound. We also obtain volume estimates in terms of the

first multiple of \(D\) having at least two independent global sections.