论文标题
通过投影几何形状来表征三次超曲面
Characterizing cubic hypersurfaces via projective geometry
论文作者
论文摘要
We use the cut and paste relation $[Y^{[2]}] = [Y][\mathbb{P}^m] + \mathbb{L}^2 [F(Y)]$ in $K_0(\text{Var}_k)$ of Galkin--Shinder for cubic hypersurfaces arising from projective geometry to characterize cubic hypersurfaces of sufficiently high dimension在某些数值或通用条件下。从所使用的数值条件中删除涉及中间贝蒂数的条件将可能的$ y $扩展到立方体超曲面，两个四边形高空的完整交集或两个四分之一的高度刺眼的完整交叉点。同样的方法还提供了其他切割和糊状关系的家族，只能通过立方体曲面来满足。
We use the cut and paste relation $[Y^{[2]}] = [Y][\mathbb{P}^m] + \mathbb{L}^2 [F(Y)]$ in $K_0(\text{Var}_k)$ of Galkin--Shinder for cubic hypersurfaces arising from projective geometry to characterize cubic hypersurfaces of sufficiently high dimension under certain numerical or genericity conditions. Removing the conditions involving the middle Betti number from the numerical conditions used extends the possible $Y$ to cubic hypersurfaces, complete intersections of two quadric hypersurfaces, or complete intersections of two quartic hypersurfaces. The same method also gives a family of other cut and paste relations that can only possibly be satisfied by cubic hypersurfaces.
