Curves on Heisenberg invariant quartic surfaces in projective 3-space

Abstract

This paper is about the family of smooth quartic surfaces $X\subset {\mathbb{P}}^3$ that are invariant under the Heisenberg group $H_{2,2}$. For a very general such surface $X$, we show that the Picard number of $X$ is 16 and determine its Picard group. It turns out that the general Heisenberg invariant quartic contains 320 smooth conics and that in the very general case, this collection of conics generates the Picard group.

Updated references, corrected typos

References in corpus (1)

• Néron-Severi groups under specialization

Cited by in corpus (2)

• A remark on the intersection of plane curves
• Components of the Hilbert scheme of space curves on low-degree smooth surfaces