On a classical correspondence between K3 surfaces II
| dc.creator | Madonna, Carlo | |
| dc.creator | Nikulin, Viacheslav V. | |
| dc.date | 2003-04-25 | |
| dc.date | 2003-07-10 | |
| dc.date.accessioned | 2026-07-07T04:57:25Z | |
| dc.date.available | 2026-07-07T04:57:25Z | |
| dc.description | Let X be a K3 surface and H a primitive polarization of degree H^2=2a^2, a>1. The moduli space of sheaves over X with the isotropic Mukai vector (a,H,a) is again a K3 surface Y which is endowed by a natural nef element h with h^2=2. We give necessary and sufficient conditions in terms of Picard lattices N(X) and N(Y) when Y\cong X, generalising our results math.AG/0206158 for a=2. E.g. we show that Y\cong X if for one of α=\pm 1,\pm 2 which is coprime to a there exists h_1\in N(X) such that h_1^2= 2αa, H\cdot h_1\equiv 0\mod αa, and the primitive sublattice [H,h_1]_{pr} \subset N(X) contains x such that $x\cdot H=1$. We find all divisorial conditions on moduli of (X,H) (i.e for Picard number 2) which imply Y\cong X and H\cdot N(X)=Z. Some of these conditions were found in different form by A.N. Tyurin in 1987. | |
| dc.description | 19 pages, no figures; Corrections and simplifications are done | |
| dc.identifier | https://arxiv.org/abs/math/0304415 | |
| dc.identifier | http://arxiv.org/abs/math/0304415 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67257 | |
| dc.subject | Algebraic Geometry | |
| dc.title | On a classical correspondence between K3 surfaces II | |
| dc.type | text |