We introduce a higher-order version of the tangent map of a morphism and find a matrix representation. We then apply this matrix to solve a conjecture by T. Yasuda regarding the semigroup of the higher Nash blowup of formal curves. We first show that the conjecture is true for toric curves. We conclude by exhibiting a family of non-monomial curves where the conjecture fails.

中文翻译：

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高阶切线图和对曲线更高纳什爆炸的猜想

我们引入了态射切图的高阶版本并找到了一个矩阵表示。然后我们应用这个矩阵来解决 T. Yasuda 关于形式曲线的更高纳什爆炸半群的猜想。我们首先证明该猜想对于复曲面是正确的。最后，我们展示了猜想失败的一系列非单项曲线。