根尖和尖
Tacnodes and cusps
摘要：
设Z是由r>5个二重点并构成的射影平面的零维子概型，I是它的定义理想层。已知当点不同且处于一般位置时，I具有期望的上同调（Hirschowitz '85）。我们通过允许无穷近点来扩展这个结果，其中一个点具有更大的多重性。作为应用，给出了具有三角结点和高阶尖点的平面曲线存在性的新的界。
英文摘要：
Let Z be a zero-dimensional subscheme of the projective plane consisting of the union of r>5 double points, I its defining ideal sheaf. It is known that I has the expected cohomology when the points are distinct and in general position (Hirschowitz '85). We extend this result by allowing infinitely near points, one of them having bigger multiplicity. As an application, new bounds are given for the existence of plane curves with tacnodes and higher order cusps.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
