论文标题
Fano歧管与Lefschetz缺陷3
Fano manifolds with Lefschetz defect 3
论文作者
论文摘要
令X成为平滑，复杂的Fano品种，Delta（X）其Lefschetz缺陷。众所周知，如果delta（x）至少为4，则x对乘积sxt是同构，其中dim t = dim x-2。在本文中，我们证明了Delta（x）= 3的情况下的结构定理。我们表明，存在一个光滑的Fano品种，带有DIM T = DIM X-2，从而从T具有两个可能的显式构建体获得X。在这两种情况下，t上都有一个p^2-bundle z，使得x是沿三个成对的不相交，不可还原的，condimimension 2 subvarieties沿三个成对脱节的爆炸。然后，我们将结构定理应用于FANO 4倍，将X具有PICARD编号5的情况，以及具有基本分区收缩的Fano品种，将除数发送到曲线。特别是，我们将FANO 4倍分类（x）= 3完成。
Let X be a smooth, complex Fano variety, and delta(X) its Lefschetz defect. It is known that if delta(X) is at least 4, then X is isomorphic to a product SxT, where dim T=dim X-2. In this paper we prove a structure theorem for the case where delta(X)=3. We show that there exists a smooth Fano variety T with dim T=dim X-2 such that X is obtained from T with two possible explicit constructions; in both cases there is a P^2-bundle Z over T such that X is the blow-up of Z along three pairwise disjoint smooth, irreducible, codimension 2 subvarieties. Then we apply the structure theorem to Fano 4-folds, to the case where X has Picard number 5, and to Fano varieties having an elementary divisorial contraction sending a divisor to a curve. In particular we complete the classification of Fano 4-folds with delta(X)=3.
