Lines on quartic surfaces

Research paper by Alex Degtyarev, Ilia Itenberg, Ali Sinan Sertöz

Indexed on: 16 Jan '16Published on: 16 Jan '16Published in: Mathematics - Algebraic Geometry


We show that the maximal number of (real) lines in a (real) nonsingular spatial quartic surface is 64 (respectively, 56). We also give a complete projective classification of all quartics containing more than 52 lines: all such quartics are projectively rigid. Any value not exceeding 52 can appear as the number of lines of an appropriate quartic.