Résume | I suggest a new approach, based on the embedding of the (modified) Néron--Severi lattice to a Niemeier lattice, to the following conjecture: *The number of tritangents to a smooth sextic is 72, 66 (each realized by a single curve), or less. The maximal number of real tritangents to a real smooth sextic is 66*. (Observed are all counts except 65 and 63.) The computation becomes much easier (linear algebra in well-studied lattices rather than abstract number theory), and it has been completed for all but Leech lattices. At present, I am 99% sure that I can eliminate the Leech lattice, settling the above conjecture. |