论文标题
恒星的曲霉几何形状
Stellahedral geometry of matroids
论文作者
论文摘要
我们使用恒星曲曲面品种的几何形状来研究成曲霉。我们确定了具有恒星复曲面品种的共同体学环的评估组，并表明了矩阵的估值，同源和数值等效关系一致。我们为Matroid的Tutte多项式建立了一个新的对数洞穴结果，回答了Wagner和Shapiro-Smirnov-vaintrob在nikov-Shapiro代数上的问题，并计算了Chern-Schwartz-Macpherson Matroid Schubert细胞类别的Chern-Schwartz-Macpherson类。中央结构是以恒定的曲曲面品种上的某些矢量束建模的“矩形的增强重言式类别”。
We use the geometry of the stellahedral toric variety to study matroids. We identify the valuative group of matroids with the cohomology ring of the stellahedral toric variety, and show that valuative, homological, and numerical equivalence relations for matroids coincide. We establish a new log-concavity result for the Tutte polynomial of a matroid, answering a question of Wagner and Shapiro-Smirnov-Vaintrob on Postnikov-Shapiro algebras, and calculate the Chern-Schwartz-MacPherson classes of matroid Schubert cells. The central construction is the "augmented tautological classes of matroids," modeled after certain vector bundles on the stellahedral toric variety.
