We establish a global Torelli theorem for the complete family of Calabi-Yau threefolds arising from cyclic triple covers of P^(3)branched along six stable hyperplanes.
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 (...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.展开更多
Let S be a complete intersection of a smooth quadric 3-fold Q and a hypersurface of degree d in P4.We analyze GIT stability of S with respect to the natural G=SO(5,C)-action.We prove that if d 4 and S has at worst sem...Let S be a complete intersection of a smooth quadric 3-fold Q and a hypersurface of degree d in P4.We analyze GIT stability of S with respect to the natural G=SO(5,C)-action.We prove that if d 4 and S has at worst semi-log canonical singularities then S is G-stable.Also,we prove that if d 3 and S has at worst semi-log canonical singularities then S is G-semistable.展开更多
The objects in this paper are all projective 3-folds over an algebresically closed field of characteristic 0. After simply generalizing the Rationality theorem, a kind of contractions. of non-minimal 3-folds is given
文摘We establish a global Torelli theorem for the complete family of Calabi-Yau threefolds arising from cyclic triple covers of P^(3)branched along six stable hyperplanes.
基金supported by the project VSHMOD-2009 ANR-09-BLAN-0104-01
文摘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.
基金supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Korea government(MSIP)(Grant No.2013006431)the National Research Foundation of Korea funded by the Korea government(MSIP)(Grant No.2013042157)
文摘Let S be a complete intersection of a smooth quadric 3-fold Q and a hypersurface of degree d in P4.We analyze GIT stability of S with respect to the natural G=SO(5,C)-action.We prove that if d 4 and S has at worst semi-log canonical singularities then S is G-stable.Also,we prove that if d 3 and S has at worst semi-log canonical singularities then S is G-semistable.
文摘The objects in this paper are all projective 3-folds over an algebresically closed field of characteristic 0. After simply generalizing the Rationality theorem, a kind of contractions. of non-minimal 3-folds is given
