论文标题
规范对称正方形的投影正态性
Projective normality of canonical symmetric squares
论文作者
论文摘要
回想一下，光滑的复杂的射击曲线在非高温时具有很大的典型束，并且根据M. Noether的定理，所产生的嵌入在预测上是正常的。培养皿的定理进一步断言，如果曲线既不是三角形也不是光滑的平面五分化，则四边形产生同质的理想。在本说明中，我们证明了Noether定理的曲线对称平方的类似物 - 即，对称平方的规范束确定曲线本身既不是过度ellelliptic，三角形，也不是光滑的平面五重奏。彼得里（Petri）的定理强调了二次创造曲线理想的统治角色。
Recall that a smooth complex projective curve has a very ample canonical bundle when it is non-hyperelliptic, and according to a theorem of M. Noether the resulting embedding is projectively normal. A theorem of Petri further asserts that the homogeneous ideal is generated by quadrics if the curve is neither trigonal nor a smooth plane quintic. In this note, we prove an analogue of Noether's theorem for the symmetric square of the curve - namely, the canonical bundle of the symmetric square determines a projectively normal embedding exactly when the curve itself is neither hyperelliptic, trigonal nor a smooth plane quintic. The theorem of Petri highlights the governing role played by quadric generation of the ideal of the curve.
