36 citations · 52 across the 10 of their papers we have counts for
10 papers
Contact Invariants for Plane Curves in a Pencil
Ciro Ciliberto, Rick Miranda, Joaquim Roe
Let $\calP$ be a general pencil of curves of degree in the projective plane. In this paper we review the computation of the number of curves in $\calP$ that have a hyperflex li…
Constructions for rational multiple planes
Ciro Ciliberto, Rick Miranda
A finite, normal cover $f: X\longrightarrow \bbP^2$ of degree (the case is well known and we do not consider it in this paper) is called \emph{simple}, if there is…
Bounds on the Mordell-Weil rank of elliptic fibrations
Antonella Grassi, Rick Miranda, Kapil Paranjape +2
We prove that the Mordell-Weil group of a higher dimensional elliptic fibration naturally embeds into that of a suitable elliptic surface. We give sufficient conditions for the exi…
Rational elliptic surfaces with six singular double fibres
Ciro Ciliberto, Antonella Grassi, Rick Miranda +2
A rational elliptic surface with section is a smooth, rational, complex, projective surface that admits a relatively minimal fibration $f: \mathcal{X}\longrightarrow…
Non-cycle triple planes with branch curve of degree at most 10
Ciro Ciliberto, Rick Miranda
In this paper we classify normal non--cyclic triple covers of $\bbP^2$ with branch curve of degree at most 10.
Boundedness Results for Planar Linear Systems Assuming The Segre-Harbourne-Gimigliano-Hirschowitz Conjecture
Ciro Ciliberto, Rick Miranda, Joaquim Roé
Let be the projective plane blown up at general points. In this paper we give several consequences of the Segre-Harbourne-Gimigliano-Hirschowitz Conjecture, that…
Variations on Pascal's Theorem
Ciro Ciliberto, Rick Miranda
In this paper we present a variety of statements that are in the spirit of the famous theorem of Pascal, often referred to as the Mystic Hexagon. We give explicit equations describ…
Quadric cones on the boundary of the Mori cone for very general blowups of the plane
Ciro Ciliberto, Rick Miranda, Joaquim Roé
We show the existence of cones over 8-dimensional rational spheres at the boundary of the Mori cone of the blow-up of the plane at very general points. This gives eviden…
Variations on Nagata's Conjecture
C. Ciliberto, B. Harbourne, R. Miranda +1
In this paper we discuss some variations of Nagata's conjecture on linear systems of plane curves. The most relevant concerns non-effectivity (hence nefness) of certain rays, which…
Degenerations of Planar Linear Systems
C. Ciliberto, R. Miranda
Fixing general points in the plane, what is the dimension of the space of plane curves of degree having multiplicity at for each ? In this article we p…