论文标题
四个空间中表面的凸面
Convex hulls of surfaces in fourspace
论文作者
论文摘要
这是对各种凸壳的代数边界的案例研究。我们专注于四个空间中的表面，以展示既不曲线也没有曲面的新几何现象。我们的方法是Ranestad和Sturmfels的通用公式进行的详细分析，如果具有低度的平滑真实代数表面（这在复数上是合理的）。我们研究Veronese，Del Pezzo和Bordiga表面的代数边界的复杂和实际特征。
This is a case study of the algebraic boundary of convex hulls of varieties. We focus on surfaces in fourspace to showcase new geometric phenomena that neither curves nor hypersurfaces do. Our method is a detailed analysis of a general purpose formula by Ranestad and Sturmfels in the case of smooth real algebraic surfaces of low degree (that are rational over the complex numbers). We study both the complex and the real features of the algebraic boundary of Veronese, Del Pezzo and Bordiga surfaces.
