• openAccess   Discrete Equivalence of Non-positive at Infinity Plane Valuations 

      Galindo, Carlos; Monserrat, Francisco; Moreno Ávila, Carlos Jesús Springer (2021-06-26)
      Non-positive at infinity valuations are a class of real plane valuations which have a nice geometrical behavior. They are divided in three types. We study the dual graphs of non-positive at infinity valuations and give ...
    • openAccess   Newton–Okounkov bodies of exceptional curve valuations 

      Galindo, Carlos; Moyano-Fernández, Julio José; Monserrat, Francisco; Nickel, Matthias European Mathematical Society (2020-03-20)
      We prove that the Newton–Okounkov body associated to the flag E∙:={X=Xr⊃Er⊃{q}}, defined by the surface X and the exceptional divisor Er given by any divisorial valuation of the complex projective plane P2, with respect ...
    • openAccess   Non-positive and negative at infinity divisorial valuations of Hirzebruch surfaces 

      Galindo, Carlos; Monserrat, Francisco; Moreno Ávila, Carlos Jesús Springer Verlag (2020-05)
      We consider rational surfaces Z defined by divisorial valuations ν of Hirzebruch surfaces. We introduce concepts of non-positivity and negativity at infinity for these valuations and prove that these concepts admit nice ...
    • openAccess   Seshadri-type constants and Newton-Okounkov bodies for non-positive at infinity valuations of Hirzebruch surfaces 

      Galindo, Carlos; Monserrat, Francisco; Moreno Ávila, Carlos Jesús Taylor and Francis (2023-02-01)
      We consider flags E• = {X ⊃ E ⊃ {q}}, where E is an exceptional divisor defining a non-positive at infinity divisorial valuation νE of a Hirzebruch surface Fδ , q a point in E and X the surface given by νE , and determine ...