8 papers
Complete subvarieties in the projectivized strata of meromorphic differentials
Dawei Chen, Guillaume Tahar
Here we give an explicit construction of a globally defined strictly plurisubharmonic function on projectivized strata of strictly meromorphic differentials with prescribed orders…
Inflection curves of rational vector fields
Boris Shapiro, Guillaume Tahar
We initiate the study of inflection curves of rational vector fields on the Riemann sphere. For a rational vector field $v_R=-R(z)\frac{\partial}{\partial z}, \qquad R(z)=\frac{Q(z…
On boundary points of minimal continuously Hutchinson invariant sets
Per Alexandersson, Nils Hemmingsson, Dmitry Novikov +2
A linear differential operator with polynomial coefficients defines a continuous family of Hutchinson operators when acting on the space of positive power…
Plane rectifiable curves: old and new
Boris Shapiro, Guillaume Tahar
In this note we recall the classical notion of an algebraically rectifiable plane curve going back to J. A. Serret, E. Laguerre and G. Humbert. We provide new criteria of algebraic…
Isoresidual curves
Dawei Chen, Quentin Gendron, Miguel Prado +1
Given a partition of , the stratum parametrizes meromorphic differential one-forms on the Riemann sphere with~ zeros and poles o…
The translation geometry of Pólya's shires
Rikard Bøgvad, Boris Shapiro, Guillaume Tahar +1
In his shire theorem, G. Pólya proves that the zeros of iterated derivatives of a meromorphic function in the complex plane accumulate on the union of edges of the Voronoi diagram…