6 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…
Bounds on the Mordell-Weil rank of elliptic fibrations
Antonella Grassi, Rick Miranda, Kapil Paranjape +2
We present two proofs for a bound on the rank of the Mordell-Weil group of some elliptic fibrations. The bounds apply to Calabi-Yau varieties, which are also of interest to the phy…
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…
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…