We present an explicit parameterization of the families of lines of the Dwork pencil of quintic threefolds. This gives rise to isomorphic curves C̃ ± φ, which parameterize the lines. These curves are 125:1 covers of genus six curves C± φ. The C± φ are first presented as curves in P1×P1 that have three nodes. It is natural to blow up P1×P1 in the three points corresponding to the nodes in order to produce smooth curves. The result of blowing up P1×P1 in three points is the quintic del Pezzo surface dP5, whose automorphism group is the permutation group S5, which is also a symmetry of the pair of curves C± φ. The subgroup A5, of even permutations, is an automorphism of each curve, where as the odd permutations.
Lines on the Dwork Pencil of Quintic Threefolds / P. Candelas, X. de la Ossa, B. van Geemen, D. van Straten. - In: ADVANCES IN THEORETICAL AND MATHEMATICAL PHYSICS. - ISSN 1095-0761. - 16:6(2012), pp. 1779-1836.
|Titolo:||Lines on the Dwork Pencil of Quintic Threefolds|
VAN GEEMEN, LAMBERTUS (Penultimo)
|Settore Scientifico Disciplinare:||Settore MAT/03 - Geometria|
|Data di pubblicazione:||2012|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.4310/ATMP.2012.v16.n6.a4|
|Appare nelle tipologie:||01 - Articolo su periodico|