论文标题
几何Manin的猜想3倍
Geometric Manin's Conjecture for Fano 3-Folds
论文作者
论文摘要
我们将自由理性曲线的家庭分类为所有平滑的Fano三倍，比复数。特别是，我们证明代表任何固定数值曲线类的非常自由的理性曲线的家族是不可还原或空的。这证明了Manin在维度三中的猜想。对于每种变形类型的一般FANO三倍，我们的结果使我们能够明确计算不可约，几何有理曲线的模量空间的组件数量，这可能不是免费的，代表任何数字类别。
We classify families of free rational curves on all smooth Fano threefolds over the complex numbers. In particular, we prove the family of very free rational curves representing any fixed numerical curve class is either irreducible or empty. This proves Geometric Manin's Conjecture in dimension three. For general Fano threefolds of each deformation type, our results allow us to explicitly count the number of components of the moduli space of irreducible, geometrically rational curves, which may not be free, representing any numerical class.
