论文标题
完整的Quadrics：高斯型号和半决赛编程的舒伯特演算
Complete quadrics: Schubert calculus for Gaussian models and semidefinite programming
论文作者
论文摘要
我们在线性浓度模型的最大似然度（ML程度）之间建立了联系，对于完整的四边形，对于线性浓度模型，半芬矿编程（SDP）的代数度（SDP）和Schubert Cilculus。我们证明了sturmfels和uhler对ML度量的多项式性的猜想。我们还证明了Nie，Ranestad和Sturmfels的猜想，为SDP程度提供了明确的公式。这三个领域之间的相互作用为列举不变性的渐近行为提供了新的启示。我们还将这些结果扩展到通用矩阵和偏斜对称矩阵的空间。
We establish connections between: the maximum likelihood degree (ML-degree) for linear concentration models, the algebraic degree of semidefinite programming (SDP), and Schubert calculus for complete quadrics. We prove a conjecture by Sturmfels and Uhler on the polynomiality of the ML-degree. We also prove a conjecture by Nie, Ranestad and Sturmfels providing an explicit formula for the degree of SDP. The interactions between the three fields shed new light on the asymptotic behaviour of enumerative invariants for the variety of complete quadrics. We also extend these results to spaces of general matrices and of skew-symmetric matrices.
