Curves on Heisenberg invariant quartic surfaces in projective 3-space

Details Curves on Heisenberg invariant quartic surfaces in projective 3-space Curves on Heisenberg invariant quartic surfaces in projective 3-space

2010-10-19

arxiv.org/abs/1010.4058v2

Mathematics

Algebraic Geometry

Added references, corrected typos

Scientific paper

This paper is about the family of smooth quartic surfaces $X \subset \PP^{3}$ 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.

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