论文标题
复曲面的极地图和特征类
Toric polar maps and characteristic classes
论文作者
论文摘要
鉴于在复杂的投影空间中的高度表面，我们证明其复曲面极地图的多边形与Chern-Schwartz-Macpherson类别的系数同意，即杰出的开放式集合，即Hypersurface和坐标均匀的互动。特别是，旋转层图的程度由杰出的开放集的符号拓扑特征给出。对于平面曲线，根据局部不变性，获得了感谢您的精确公式。最后，我们以任意维度的家庭为家庭建立了不可约形的超曲面，其曲折的极地图是生育的。
Given a hypersurface in a complex projective space, we prove that the multidegrees of its toric polar map agree, up to sign, with the coefficients of the Chern-Schwartz-MacPherson class of a distinguished open set, namely the complement of the union of the hypersurface and the coordinate hyperplanes. In particular, the degree of the toric polar map is given by the signed topological Euler characteristic of the distinguished open set. For plane curves, a precise formula for the degree of the toric polar map is obtained in terms of local invariants. Finally, we construct families, in arbitrary dimension, of irreducible hypersurfaces whose toric polar map is birational.
