论文标题
在表面上曲线的节点多项式
Node Polynomials for Curves on Surfaces
论文作者
论文摘要
我们完成了我们宣布的定理的证明，并部分证明了[数学。 nachr。 271（2004），69-90，Math.ag/0111299]。定理涉及一个曲线家庭在一个表面家庭上。它有两个部分。第一个是在该论文中证明的。它描述了一个自然循环，该循环列举了恰好$ r $普通节点的家庭曲线。第二部分在这里证明。它断言，对于$ r \ le 8 $，该周期的类别是由可计算的通用多项式在对家族班级产品的参数空间的俯卧撑中给出的。
We complete the proof of a theorem we announced and partly proved in [Math. Nachr. 271 (2004), 69-90, math.AG/0111299]. The theorem concerns a family of curves on a family of surfaces. It has two parts. The first was proved in that paper. It describes a natural cycle that enumerates the curves in the family with precisely $r$ ordinary nodes. The second part is proved here. It asserts that, for $r\le 8$, the class of this cycle is given by a computable universal polynomial in the pushdowns to the parameter space of products of the Chern classes of the family.
