论文标题
对曲ic品种中的对和noether-lefschetz位点的变形
Deformation of pairs and Noether-Lefschetz loci in toric varieties
论文作者
论文摘要
我们继续研究noethe-lefschetz基因群中的多种多样的品种，并研究对（v，x）的变形（v，x），其中v是一个完整的交点，在一个奇怪的尺寸简单的图谱中，与v \ supptions相关的x。且仅当V保持代数时，在无限变形下类型（k，k）。实际上，我们证明本地Noether-Lefschetz基因座是合适的希尔伯特方案的不可约组成部分。这在我们以前的工作[4]中概括了定理4.2，而Dan在[10]中证明了主要定理。
We continue our study of the Noether-Lefschetz loci in toric varieties and investigate deformation of pairs (V,X) where V is a complete intersection subvariety and X a quasi-smooth hypersurface in a odd dimensional simplicial projective toric variety, with V\subset X. Under some assumptions, we prove that the cohomological class in H^{k,k}(X) associated to V remains of type (k,k) under an infinitesimal deformation if and only if V remains algebraic. Actually we prove that locally the Noether-Lefschetz locus is an irreducible component of a suitable Hilbert scheme. This generalizes Theorem 4.2 in our previous work [4] and the main theorem proved by Dan in [10].
