论文标题
非鼻实际平面有理曲线的枚举
Enumeration of non-nodal real plane rational curves
论文作者
论文摘要
Welschinger不变式列举了平面或另一个真理表面中的真实节点有理曲线。我们分析了相似的枚举不变性的存在，这些不变性数量是规定了非节点奇点的实际有理平面曲线，并通过了平面中许多点的适当点的通用共轭不变构型。我们表明，像这样的不变是独一无二的：它列举了通过一般选择的四对复杂的共轭点，列举了真实的三个占领四分之一。因此，我们表明，通过对四对复杂共轭点的任何通用配置，人们总是可以追踪一对真实的三个占领四重奏。
Welschinger invariants enumerate real nodal rational curves in the plane or in another real rational surface. We analyze the existence of similar enumerative invariants that count real rational plane curves having prescribed non-nodal singularities and passing through a generic conjugation-invariant configuration of appropriately many points in the plane. We show that an invariant like this is unique: it enumerates real rational three-cuspidal quartics that pass through generically chosen four pairs of complex conjugate points. Consequently, we show that through any generic configuration of four pairs of complex conjugate points, one can always trace a pair of real rational three-cuspidal quartics.
