论文标题
超曲面的投影单构
Monodromy of projections of hypersurfaces
论文作者
论文摘要
让$ x $成为不可约，减少的复杂的投射超出表面为$ d $。如果$ x $中未包含的点$ p $，则称为统一，如果从$ p $的$ x $投影的单体组组对对称组$ s_d $是同构的。我们证明，当$ x $平滑或流畅的多样性投影时，非均匀点的轨迹是有限的。总的来说，它包含在一个有限的编成二拟合线性空间中，至少$ 2 $，除了可能用于一类特殊类别的Hypersurfaces，具有奇异基因座的奇异基因座线性，以consimimension $ 1 $。此外，我们概括了福川和高桥对加洛伊斯积分的有限性的结果。
Let $X$ be an irreducible, reduced complex projective hypersurface of degree $d$. A point $P$ not contained in $X$ is called uniform if the monodromy group of the projection of $X$ from $P$ is isomorphic to the symmetric group $S_d$. We prove that the locus of non--uniform points is finite when $X$ is smooth or a general projection of a smooth variety. In general, it is contained in a finite union of linear spaces of codimension at least $2$, except possibly for a special class of hypersurfaces with singular locus linear in codimension $1$. Moreover, we generalise a result of Fukasawa and Takahashi on the finiteness of Galois points.
