Families of blowups of the real affine plane: classification, isotopies and visualization (Q2229748)

Motivated by didactic visualizations of blowups, the authors ask whether two oriented isomorphic embedded blowups of the real affine plane over a finite point set \(Z\) can be connected by a continuous family of like blowups. The answer is affirmative and a construction of connecting families based on a connectivity result in terms of matrix polynomials is presented. Moreover, the authors prove that two embedded blowups are oriented isomorphic if and only if they have equal sign distribution on~\(Z\). Using previously developed visualization techniques, a continuous interactive deformation between two isomorphic blowups can be visualized in real time. The paper at hand illustrates this with several enlightening picture series.