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
In this paper, we establish a Second Main Theorem for an algebraically degenerate holomorphic curve f : C → Pn(C) intersecting hypersurfaces in general position. The related Diophantine problems are also considered.
We give an improvement for the second main theorem of algebraically non-degenerate holomorphic curves into a complex projective variety V intersecting hypersurfaces in subgeneral position, obtained by Chen et al.(2012...We give an improvement for the second main theorem of algebraically non-degenerate holomorphic curves into a complex projective variety V intersecting hypersurfaces in subgeneral position, obtained by Chen et al.(2012). An explicit estimate for the truncation level is also obtained in the projective normal case.展开更多
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 National Natural Science Foundation of China (Grant Nos. 11171255, 10901120)Doctoral Program Foundation of the Ministry of Education of China (Grant No.20090072110053)US National Security Agency (Grant Nos. H98230-09-1-0004, H98230-11-1-0201)
文摘In this paper, we establish a Second Main Theorem for an algebraically degenerate holomorphic curve f : C → Pn(C) intersecting hypersurfaces in general position. The related Diophantine problems are also considered.
基金supported by National Natural Science Foundation of China(Grant No.11371139)National Security Agency of the USA(Grant No.H98230-11-1-0201)
文摘We give an improvement for the second main theorem of algebraically non-degenerate holomorphic curves into a complex projective variety V intersecting hypersurfaces in subgeneral position, obtained by Chen et al.(2012). An explicit estimate for the truncation level is also obtained in the projective normal case.
