论文标题
概率的枚举几何形状超过$ p $ - 加法数：完整交叉点上的线性空间
Probabilistic enumerative geometry over $p$-adic numbers: linear spaces on complete intersections
论文作者
论文摘要
我们计算在$ p $ -ADIC投影空间中随机完整交叉点上线性空间数量的期望。在这里，“随机”意味着定义完整交叉点的多项式的系数均匀地形成$ p $ - adic整数。我们表明，随着Prime $ P $倾向于无限，随机完整交叉路口上的预期线性空间数量往往$ 1 $。如果在三个空间中随机立方体上的线数和四个空间中两个随机尺度的交点上，我们给出了一个明确的公式。
We compute the expectation of the number of linear spaces on a random complete intersection in $p$-adic projective space. Here "random" means that the coefficients of the polynomials defining the complete intersections are sampled uniformly form the $p$-adic integers. We show that as the prime $p$ tends to infinity the expected number of linear spaces on a random complete intersection tends to $1$. In the case of the number of lines on a random cubic in three-space and on the intersection of two random quadrics in four-space, we give an explicit formula for this expectation.
