barth, nieto, quintic, algebraic, geometry, quintic, fold, sometimes, dimensional, projective, space, studied, wolf, barth, isidro, nieto, 1994, that, hessian, segre, cubic, definition, editthe, closure, points, satisfying, equations, displaystyle, displaystyl. In algebraic geometry the Barth Nieto quintic is a quintic 3 fold in 4 or sometimes 5 dimensional projective space studied by Wolf Barth and Isidro Nieto 1994 that is the Hessian of the Segre cubic Definition editThe Barth Nieto quintic is the closure of the set of points x0 x1 x2 x3 x4 x5 of P5 satisfying the equations x 0 x 1 x 2 x 3 x 4 x 5 0 displaystyle displaystyle x 0 x 1 x 2 x 3 x 4 x 5 0 nbsp x 0 1 x 1 1 x 2 1 x 3 1 x 4 1 x 5 1 0 displaystyle displaystyle x 0 1 x 1 1 x 2 1 x 3 1 x 4 1 x 5 1 0 nbsp Properties editThe Barth Nieto quintic is not rational but has a smooth model that is a modular Calabi Yau manifold with Kodaira dimension zero Furthermore it is birationally equivalent to a compactification of the Siegel modular variety A1 3 2 1 References edit Hulek Klaus Sankaran Gregory K 2002 The geometry of Siegel modular varieties Higher dimensional birational geometry Kyoto 1997 Advanced Studies in Pure Mathematics Vol 35 Tokyo Math Soc Japan pp 89 156 doi 10 2969 aspm 03510089 MR 1929793 Barth Wolf Nieto Isidro 1994 Abelian surfaces of type 1 3 and quartic surfaces with 16 skew lines Journal of Algebraic Geometry 3 2 173 222 ISSN 1056 3911 MR 1257320 nbsp This algebraic geometry related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Barth Nieto quintic amp oldid 925370756, wikipedia, wiki, book, books, library,
