The Remark on Discriminants of K3 Surfaces Moduli as Sets of Zeros of Automorphic Forms
| dc.creator | Nikulin, Viacheslav V. | |
| dc.date | 1995-12-29 | |
| dc.date | 1996-01-03 | |
| dc.date.accessioned | 2026-07-07T08:58:05Z | |
| dc.date.available | 2026-07-07T08:58:05Z | |
| dc.description | We show that for any $N>0$ there exists a natural even $n>N$ such that the discriminant of moduli of K3 surfaces of the degree $n$ is not equal to the set of zeros of any automorphic form on the corresponding IV type domain. We give the necessary condition on a "condition $S\subset L_{K3}$ on Picard lattice of K3'' for the corresponding moduli $\M_{S\subset L_{K3}}$ of K3 to have the discriminant which is equal to the set of zeros of an automorphic form. We conjecture that the set of $S\subset L_{K3}$ satisfying this necessary condition is finite if $\rk S \le 17$. We consider this finiteness conjecture as "mirror symmetric'' to the known finiteness results for arithmetic reflection groups in hyperbolic spaces and as important for the theory of Lorentzian Kac--Moody algebras and the related theory of automorphic forms. | |
| dc.description | AMSTeX, 6 pages, no figures. More exact formulations are given | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9512018 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9512018 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/147182 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Quantum Algebra | |
| dc.subject | 14D20; 10D20; 17B65 | |
| dc.title | The Remark on Discriminants of K3 Surfaces Moduli as Sets of Zeros of Automorphic Forms | |
| dc.type | text |