Intersection of arcs and normal rational curves in spaces of even characteristic (Q1339791)

The \((k + 1)\)-arcs \(K\) in \(PG(n,q)\), \(q\) even, which have \(k\) points in common with a given rational curve \(L\) of \(PG(n,q)\) are studied in detail. It is proved that, for \(q \geq q_ 0\), \(| K \cap L| \leq (q + 4)/2\) when \(n = 3\) and \(| K \cap L | \leq (q + 2)/2\) when \(4 \leq n \leq 0.09q + 2.59\), improving previous results. This is used to give a complete characterization of arcs of \(PG(n,q)\), \(q\) even and \(q \geq q_ 0\), having at least \(0.41(q + 1)\) or \(0,41q + n - 1.59\) points in common with \(L\) according to \(n = 3\) or \(4 \leq n \leq 0.09q + 2.59\).