The Coble hypersurfaces
代数几何
2007-05-23 v1
摘要
Let A be an indecomposable principally polarized abelian variety of dimension g . Third order theta functions embed A in a projective space P(V_3), while second order theta functions embed the Kummer variety K=A/<-1> in a projective space P(V_2). Coble observed that for g = 2 there is a unique cubic hypersurface in P(V_3) that is singular along A, and for g = 3 a unique quartic hypersurface in P(V_2) singular along K . We explain these facts by a simple analysis of the representations of the corresponding Heisenberg group.
引用
@article{arxiv.math/0306097,
title = {The Coble hypersurfaces},
author = {Arnaud Beauville},
journal= {arXiv preprint arXiv:math/0306097},
year = {2007}
}
备注
6 pages