熱帶幾何相交理論與熱帶循環之研究(II)

Abstract

本計畫承接去年計畫, 研究熱帶幾何相交理論。我們正進行的計畫, 是研究熱帶相交之相關理論, 及熱帶代數簇之計算方式。在這個計畫中, 我們會以熱帶幾何的角度, 去研究萊夫謝茨束及流形退化的問題。主要的關鍵是要使用熱帶幾何去研究非交換餘調。我們準備發展一個叫「非交換餘調熱帶化」的技巧, 並希望能應用這新的技術, 研究單值作用。為達到我們的目標, 我們需要深入理解熱帶相交理論, 並且能計算熱帶簇。我們會用進行中計畫得到的成果, 在這個計畫中實際應用出來。

The project is a continuation of our previous project. Our on-going project is to learn basic theory of the tropical intersection theory, as well as the computing techniques of tropical varieties. In this project, we will apply what we learn to study Lefschetz pencils and manifold degenerations in tropical settings. A key point is to apply tropical geometry to study non-abelian cohomology. We would like to develop a new technique, which we call ""tropicalization of non-abelian chomology,`` to study monodromy actions. To achieve our goal, we need to comprehend tropical intersection theory and tropical cycles, as well as the ability to compute tropical algebraic variety. We would like to apply what we learn from our on-going project to this new project.