• openAccess   Algebraic integrability of planar polynomial vector fields by extension to Hirzebruch surfaces 

      Galindo, Carlos; Monserrat, Francisco; Pérez-Callejo, Elvira Springer Nature (2022-09-18)
      We study algebraic integrability of complex planar polynomial vector fields X=A(x,y)(∂/∂x)+B(x,y)(∂/∂y) through extensions to Hirzebruch surfaces. Using these extensions, each vector field X determines two infinite families ...
    • openAccess   On the Degree of Curves with Prescribed Multiplicities and Bounded Negativity 

      Galindo, Carlos; Moreno Ávila, Carlos Jesús; Pérez-Callejo, Elvira; Montserrat Delpalillo, Francisco José Oxford University Press (2022-07-28)
      We provide a lower bound on the degree of curves of the projective plane P2 passing through the centers of a divisorial valuation ν of P2 with prescribed multiplicities, and an upper bound for the Seshadri-type constant ...