• openAccess   Newton–Okounkov Bodies of Exceptional Curve Plane Valuations Non-positive at Infinity 

      Galindo, Carlos; Montserrat Delpalillo, Francisco José; Moyano-Fernández, Julio José; Nickel, Matthias Springer (2018-11-04)
      In this note we announce a result determining the Newton–Okounkov bodies of the line bundle OP2(1) with respect to exceptional curve plane valuations non-positive at infinity.
    • openAccess   On the computation of Darboux first integrals of a class of planar polynomial vector fields 

      Ferragut, Antoni; Galindo, Carlos; Montserrat Delpalillo, Francisco José Elsevier (2019-05)
      We study the class of planar polynomial vector fields admitting Darboux first integrals of the type I I r i=1 fiαi , where the αi 's are positive real numbers and the fi 's are polynomials defining curves with only one ...
    • 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 ...
    • openAccess   The Poincaré Polynomial of a Linear Code 

      Galindo, Carlos; Hernando, Fernando; Montserrat Delpalillo, Francisco José; Pellikaan, Ruud Springer (2018-09-19)
      We introduce the Poincaré polynomial of a linear q-ary code and its relation to the corresponding weight enumerator. The question of whether the Poincaré polynomial is a complete invariant is answered affirmatively for ...
    • openAccess   The Poincaré problem, algebraic integrability and dicritical divisors 

      Galindo, Carlos; Montserrat Delpalillo, Francisco José (2015-07-01)
      We solve the Poincaré problem for plane foliations with only one dicritical divisor. Moreover, in this case, we give a simple algorithm that decides whether a foliation has a rational first integral and computes it in the ...