Laura DeMarco

collaborators

3 papers

math.DS2024

The geometry of preperiodic points in families of maps on $P^{N}$

Laura DeMarco, Niki Myrto Mavraki

We study the dynamics of algebraic families of maps on $P^{N}$ , over the field $C$ of complex numbers, and the geometry of their preperiodic points. The goal of thi…

math.DS2024

Bounded geometry for PCF-special subvarieties

Laura DeMarco, Niki Myrto Mavraki, Hexi Ye

For each integer $d \geq 2$ , let $M_{d}$ denote the moduli space of maps $f : P^{1} \to P^{1}$ of degree $d$ . We study the geometric configurations of subsets of postcriti…

math.DS2023

Geometry of PCF parameters in spaces of quadratic polynomials

Laura DeMarco, Niki Myrto Mavraki

We study algebraic relations among postcritically finite (PCF) parameters in the family $f_{c} (z) = z^{2} + c$ . Ghioca, Krieger, Nguyen and Ye proved that an algebraic curve in $\mathb…

The geometry of preperiodic points in families of maps on PN

Bounded geometry for PCF-special subvarieties

Geometry of PCF parameters in spaces of quadratic polynomials

The geometry of preperiodic points in families of maps on $P^{N}$