论文标题
半光滑品种的变形
Deformations of semi-smooth varieties
论文作者
论文摘要
对于一个单数x，确定其平稳性和研究其变形的重要步骤是对切线捆和捆t^1_x的理解：= ext^1（omega_x，o_x）。 如果其奇异性是典型的典范，则是半平滑的，是仿射空间的双重交叉点（UV = 0）的乘积（UV = 0）或捏点（u^2-v^2w = 0）；同等地，如果可以通过平滑的互动沿光滑的除数粘合光滑的品种，以获得光滑的商品。 我们的主要结果是根据胶合数据的半平滑度X的切线捆和捆T^1_x的明确计算。
For a singular variety X, an essential step to determine its smoothability and study its deformations is the understanding of the tangent sheaf and of the sheaf T^1_X:=ext^1(Omega_X,O_X). A variety is semi-smooth if its singularities are étale locally the product of a double crossing point (uv=0) or a pinch point (u^2-v^2w=0) with affine space; equivalently, if it can be obtained by gluing a smooth variety along a smooth divisor via an involution with smooth quotient. Our main result is the explicit computation of the tangent sheaf and the sheaf T^1_X for a semi-smooth variety X in terms of the gluing data.
