On nodal prime Fano threefolds of degree 10  

作　　者：DEBARRE Olivier ILIEV Atanas MANIVEL Laurent 

机构地区：[1]Dpartement de Mathmatiques et Applications,UMR CNRS 8553,cole Normale Suprieure,45 rue d'Ulm,75230 Paris cedex 05,France [2]Department of Mathmetics,Seoul National University,Gwanak Compus,Bldg.27,Seoul 151-747,Korea [3]Institut Fourier,Universitè de Grenoble I et CNRS,BP 74,38402 Saint-Martin d'Hères,France

出　　处：《Science China Mathematics》2011年第8期1591-1609,共19页中国科学：数学（英文版）

基　　金：supported by the project VSHMOD-2009 ANR-09-BLAN-0104-01

摘　　要：We study the geometry and the period map of nodal complex prime Fano threefolds with index 1 and degree 10.We show that these threefolds are birationally isomorphic to Verra threefolds,i.e.,hypersurfaces of bidegree (2,2) in P2 × P2.Using Verra's results on the period map for these threefolds and on the Prym map for double tale covers of plane sextic curves,we prove that the fiber of the period map for our nodal threefolds is the union of two disjoint surfaces,for which we give several descriptions.This result is the analog in the nodal case of a result of Debarre O,Iliev A,Manivel L (arXiv:0812.3670) in the smooth case.We study the geometry and the period map of nodal complex prime Fano threefolds with index 1 and degree 10.We show that these threefolds are birationally isomorphic to Verra threefolds,i.e.,hypersurfaces of bidegree （2,2） in P2 × P2.Using Verra＇s results on the period map for these threefolds and on the Prym map for double tale covers of plane sextic curves,we prove that the fiber of the period map for our nodal threefolds is the union of two disjoint surfaces,for which we give several descriptions.This result is the analog in the nodal case of a result of Debarre O,Iliev A,Manivel L （arXiv：0812.3670） in the smooth case.

关 键 词：Fano threefolds period map Torelli proldem Prym varieties intermediate Jacobian nets of quadrics 

分 类 号：O187[理学—数学]