论文标题
拉格朗日的曲霉几何形状
Lagrangian geometry of matroids
论文作者
论文摘要
我们介绍了一个曲霉M的串联粉丝，这是M.伯格曼迷的一个拉格朗日类似物。我们使用孔子粉丝对M.的Chern-Schwartz-Macpherson循环进行了Lagrangian的解释。这使M.这使我们能够表达出M的h-vector，以表达M的h-vector of M. conormal of the Conorm of the Conormal of M.我们的h-vector。 Fan满足了Poincaré二元性，硬Lefschetz定理和Hodge-Riemann关系。当M的Chern-Schwartz-Macpherson循环与M的共同关系的奇特 - 里曼关系结合在一起时，MACCHWARTZ-MACPHERSON的解释意味着Brylawski's and Dawson的猜想表明，破碎电路复合物的H-媒介和M的独立性复合物是登录磁场序列。
We introduce the conormal fan of a matroid M, which is a Lagrangian analog of the Bergman fan of M. We use the conormal fan to give a Lagrangian interpretation of the Chern-Schwartz-MacPherson cycle of M. This allows us to express the h-vector of the broken circuit complex of M in terms of the intersection theory of the conormal fan of M. We also develop general tools for tropical Hodge theory to prove that the conormal fan satisfies Poincaré duality, the hard Lefschetz theorem, and the Hodge-Riemann relations. The Lagrangian interpretation of the Chern-Schwartz-MacPherson cycle of M, when combined with the Hodge-Riemann relations for the conormal fan of M, implies Brylawski's and Dawson's conjectures that the h-vectors of the broken circuit complex and the independence complex of M are log-concave sequences.
