It is known that any periodic map of order n on a closed oriented surface of genus g can be equivariantly embedded into S^(m)for some m.In the orientable and smooth category,we determine the smallest possible m when n...It is known that any periodic map of order n on a closed oriented surface of genus g can be equivariantly embedded into S^(m)for some m.In the orientable and smooth category,we determine the smallest possible m when n≥3g.We show that for each integer k>1,there exist infinitely many periodic maps such that the smallest possible m is equal to k.展开更多
In this paper, we study the possibilities for several kinds of topological, locally linear cyclic group actions of non-prime order on some closed, simply connected 4-manifolds with indefinite intersection form. Especi...In this paper, we study the possibilities for several kinds of topological, locally linear cyclic group actions of non-prime order on some closed, simply connected 4-manifolds with indefinite intersection form. Especially, we discuss the existence of locally linear pseudofree C9 action on this kind of 4-manifolds.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
Recently, we proved the Griffiths conjecture on the boundedness of the period maps, and then used it to prove global Torelli theorem on the Torelli space under certain natural conditions. This paper serves as a review...Recently, we proved the Griffiths conjecture on the boundedness of the period maps, and then used it to prove global Torelli theorem on the Torelli space under certain natural conditions. This paper serves as a review of these results and an introduction to the main ideas behind the proofs.展开更多
We consider the deformations of complex orbifolds with the underlying smooth structures being fixed.As a corollary,we can prove that the deformations of a Calabi-Yau orbifold is unobstructed by using standard argument...We consider the deformations of complex orbifolds with the underlying smooth structures being fixed.As a corollary,we can prove that the deformations of a Calabi-Yau orbifold is unobstructed by using standard arguments.Then we consider the period map for a family of complex Kahler orbifolds.We prove that the period map is holomorphic,horizontal and consistent with our Kodaira-Spencer map.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.12131009 and 12371067)Science and Technology Commission of Shanghai Municipality(Grant No.22DZ2229014)supported by National Key R&D Program of China(Grant No.2020YFA0712800)。
文摘It is known that any periodic map of order n on a closed oriented surface of genus g can be equivariantly embedded into S^(m)for some m.In the orientable and smooth category,we determine the smallest possible m when n≥3g.We show that for each integer k>1,there exist infinitely many periodic maps such that the smallest possible m is equal to k.
基金The Science and Technology Program(20110035) of Shanghai Maritime University
文摘In this paper, we study the possibilities for several kinds of topological, locally linear cyclic group actions of non-prime order on some closed, simply connected 4-manifolds with indefinite intersection form. Especially, we discuss the existence of locally linear pseudofree C9 action on this kind of 4-manifolds.
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.
文摘Recently, we proved the Griffiths conjecture on the boundedness of the period maps, and then used it to prove global Torelli theorem on the Torelli space under certain natural conditions. This paper serves as a review of these results and an introduction to the main ideas behind the proofs.
基金supported by Science Foundation of Zhejiang Sci-Tech University(ZSTU)(Grant No.17062079-Y)
文摘We consider the deformations of complex orbifolds with the underlying smooth structures being fixed.As a corollary,we can prove that the deformations of a Calabi-Yau orbifold is unobstructed by using standard arguments.Then we consider the period map for a family of complex Kahler orbifolds.We prove that the period map is holomorphic,horizontal and consistent with our Kodaira-Spencer map.
