标题： 雅可比理想的一个最小解对于一个一般曲线排列 显示英文标题

标题： A minimal resolution for the Jacobian ideal of a generic curve arrangement

摘要： 我们考虑复射影平面上的一个节点曲线$C$，其不可约分支$C_i$是光滑的。 使用 Th. Kahle、H. Schenck、B. Sturmfels 和 M. Wiesmann 关于似然对应性的最新结果，描述了$C$的雅可比理想的第一和第二交错模的最小生成元集合$G$。 $G$的元素在$f_i=0$的方程方面有显式公式，这些方程是$C$的不可约分支$C_i$。 类似的结果，包括在$\mathbb{P}^n$中超曲面排列的扩展，由 R. Burity, Z. Ramos, A. Simis 和 St. Toh\u aneanu 在一个可能在实践中不易检验的通用性假设下获得。 显示英文摘要

摘要： We consider a nodal curve $C$ in the complex projective plane whose irreducible components $C_i$ are smooth. A minimal set of generators $G$ for the first and second syzygy modules of the Jacobian ideal of $C$ are described, using recent results by Th. Kahle, H. Schenck, B. Sturmfels and M. Wiesmann on the likelihood correspondence. The elements of $G$ have explicit formulas in terms of the equations $f_i=0$ of the irreducible components $C_i$ of $C$. Similar results, including extensions to hypersurfaces arrangements in $\mathbb{P}^n$ were obtained by R. Burity, Z. Ramos, A. Simis and St. Toh\u aneanu with a genericity assumption which may not be easy to test in practice.