两个全实曲面并在其交线处的局部多项式凸性
Local polynomial convexity of the union of two totally real surfaces at their intersection
摘要：
我们考虑以下问题：设$S_1$和$S_2$是$\mathbb{C}^2$中包含原点的两个光滑的全实曲面。如果它们的切面的并集在原点是局部多项式凸的，那么$S_1 \cup S_2$在原点是局部多项式凸的吗？如果是$T_0S_1 \cap T_0S_2=\{0\}$，那么民间的结果是答案是肯定的。我们讨论了对推定证据的阻碍，并提供了一种不同的方法。当实数域上的$T_0S_1 \cap T_0S_2$的维数为1时，给出了一个几何条件，在此条件下上述问题不存在一致的答案.然后，我们讨论的条件下，我们可以期望局部多项式凸。
英文摘要：
We consider the following question: Let $S_1$ and $S_2$ be two smooth, totally-real surfaces in $\mathbb{C}^2$ that contain the origin. If the union of their tangent planes is locally polynomially convex at the origin, then is $S_1 \cup S_2$ locally polynomially convex at the origin? If $T_0S_1 \cap T_0S_2=\{0\}$, then it is a folk result that the answer is yes. We discuss an obstruction to the presumed proof, and provide a different approach. When dimension of $T_0S_1 \cap T_0S_2$ over the field of real numbers is 1, we present a geometric condition under which no consistent answer to the above question exists. We then discuss conditions under which we can expect local polynomial convexity.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
