论文标题
代数能力
Algebraic capacities
论文作者
论文摘要
我们研究来自表面上NEF除数的某些优化问题的不变性。这些优化问题是在作者的工作和合作者的工作中引起的，将障碍物绑定到符号4个manifolds之间的嵌入到（可能是单数）代数表面的积极性问题上。我们为这些不变的人开发了一般框架，并证明了其结构和渐近学的基础结果。我们描述了这些不变性与嵌入式接触同源性（ECH）的连接和在符号几何形状中不变的连接，以及在最小超丘角的研究中与最小宽度的最小宽度。我们使用这些连接中的第一个连接来获得许多复曲域域的ECH能力的子领导渐近造型的最佳边界。
We study invariants coming from certain optimisation problems for nef divisors on surfaces. These optimisation problems arise in work of the author and collaborators tying obstructions to embeddings between symplectic 4-manifolds to questions of positivity for (possibly singular) algebraic surfaces. We develop the general framework for these invariants and prove foundational results on their structure and asymptotics. We describe the connections these invariants have to Embedded Contact Homology (ECH) and the Ruelle invariant in symplectic geometry, and to min-max widths in the study of minimal hypersurfaces. We use the first of these connections to obtain optimal bounds for the sub-leading asymptotics of ECH capacities for many toric domains.
