In this paper,we study Miyaoka-type inequalities on Chern classes of terminal projective 3-folds with nef anti-canonical divisors.Let X be a terminal projective 3-fold such that-KX is nef.We show that if c_(1)(X)·...In this paper,we study Miyaoka-type inequalities on Chern classes of terminal projective 3-folds with nef anti-canonical divisors.Let X be a terminal projective 3-fold such that-KX is nef.We show that if c_(1)(X)·c_(2)(X)≠0,then c_(1)(X)·c_(2)(X)≥1/252;if further X is not rationally connected,then c_(1)(X)·c_(2)(X)≥4/5 and this inequality is sharp.In order to prove this,we give a partial classification of such varieties along with many examples.We also study the nonvanishing of c_(1)(X)^(dim X-2)·c_(2)(X)for terminal weak Fano varieties and prove a Miyaoka-Kawamata-type inequality.展开更多
In this note,we show that the solution of Kähler-Ricci flow on every Fano threefold from Family No.2.23 in the Mori-Mukai’s list develops type II singularity.In fact,we show that no Fano threefold from Family No...In this note,we show that the solution of Kähler-Ricci flow on every Fano threefold from Family No.2.23 in the Mori-Mukai’s list develops type II singularity.In fact,we show that no Fano threefold from Family No.2.23 admits Kähler-Ricci soliton and the Gromov-Hausdorff limit of the Kähler-Ricci flow must be a singular Q-Fano variety.This gives new examples of Fano manifolds of the lowest dimension on which Kähler-Ricci flow develops type II singularity.展开更多
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
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.
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
基金supported by National Natural Science Foundation of China for Innovative Research Groups(Grant No.12121001)National Key Research and Development Program of China(Grant No.2020YFA0713200)supported by Grant-in-Aid for Early Career Scientists(Grant No.22K13907)。
文摘In this paper,we study Miyaoka-type inequalities on Chern classes of terminal projective 3-folds with nef anti-canonical divisors.Let X be a terminal projective 3-fold such that-KX is nef.We show that if c_(1)(X)·c_(2)(X)≠0,then c_(1)(X)·c_(2)(X)≥1/252;if further X is not rationally connected,then c_(1)(X)·c_(2)(X)≥4/5 and this inequality is sharp.In order to prove this,we give a partial classification of such varieties along with many examples.We also study the nonvanishing of c_(1)(X)^(dim X-2)·c_(2)(X)for terminal weak Fano varieties and prove a Miyaoka-Kawamata-type inequality.
文摘In this note,we show that the solution of Kähler-Ricci flow on every Fano threefold from Family No.2.23 in the Mori-Mukai’s list develops type II singularity.In fact,we show that no Fano threefold from Family No.2.23 admits Kähler-Ricci soliton and the Gromov-Hausdorff limit of the Kähler-Ricci flow must be a singular Q-Fano variety.This gives new examples of Fano manifolds of the lowest dimension on which Kähler-Ricci flow develops type II singularity.
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.
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
