Some real and unreal enumerative geometry for flag manifolds
Frank Sottile
我们介绍了一种通用方法,用于构建对枚举几何学中的一些问题的实际解决方案,该方法提供了最大数量的实际解决方案的下限。 我们应用这种方法来表明,国旗歧管上的两个新的枚举几何问题可能所有的解决方案都是真实的,并修改这种方法,以表明另一个类可能没有真正的解决方案,这是一个新现象。 该方法起源于一种适应Grassmannians上特殊舒伯特演算的数值同源延续算法,原则上提供了最佳的数值同源算法,用于寻找这些其他枚举问题的明确解决方案。
We present a general method for constructing real solutions to some problems in enumerative geometry which gives lower bounds on the maximum number of real solutions. We apply this method to show that two new classes of enumerative geometric problems on flag manifolds may have all their solutions be real and modify this method to show that another class may have no real solutions, which is a new phenomenon. This method originated in a numerical homotopy continuation algorithm adapted to the spec...
