**Edoardo Ballico, Changho Keem**

## Quadric Hypersurfaces Containing a
Projectively Normal Curve

**Abstract:**

Let $C \subset {\bf {P}}^n$ be a smooth projectively normal curve. Let $Z$ be
the scheme-theoretic base locus of $H^0({\bf {P}}^n,\mathcal {I}_C(2))$ and $Z'$
the connected component of $Z$ containing $C$. Here we show that $Z'=C$ in
certain cases (e.g., non-special line bundles with degree near to $2p_a(C)-2$ or
certain special line bundles on general $k$-gonal curves).

**Keywords:**

Quadric hypersurfaces, $k$-gonal curves, gonality, projective normality,
normally generated line bundle.

**MSC 2000:** 14H45, 14H50