Spinor states of real rational curves in real algebraic convex 3-manifolds and enumerative invariants
Spinor states of real rational curves in real algebraic convex 3-manifolds and enumerative invariants
复制标题
实代数凸3-流形中实有理曲线的旋量态和枚举不变量
DOI：
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发表时间：
2003
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通讯作者：
Jean
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文献类型：
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作者：
Jean
设X是实代数凸3-流形，其实部具有Pin I结构。证明了实部为非空的不可约实有理曲线都有一个标准旋量态，属于f§1g。其主要结果是，在给定的数值等价类中，通过适当数目的点的实不可约有理曲线的数目的代数计数不依赖于点的实集合的选择，只要这些曲线相对于它们的旋量状态被计数。这些不变量提供了这样的实有理曲线的总数的下界，而与点的实点的选择无关。
Let X be a real algebraic convex 3-manifold whose real part is equipped with a Pin i structure. We show that every irreducible real rational curve with non-empty real part has a canonical spinor state belonging to f§1g. The main result is then that the algebraic count of the number of real irreducible rational curves in a given numerical equivalence class passing through the appropriate number of points does not depend on the choice of the real conflguration of points, provided that these curves are counted with respect to their spinor states. These invariants provide lower bounds for the total number of such real rational curves independantly of the choice of the real conflguration of points.