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arXiv · 1804.11050

Higher Nash Blowups of $A_3$-Singularity

Rin Toh-Yama
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Abstract

We show that the $ n $-th Nash blowup of the toric surface singularity of type $ A_3 $ is singular for any $ n > 0 $. It was known that the normalization of the $ n $-th Nash blowup of a toric variety is also a toric variety associated to the Gr\"{o}bner fan of a certain ideal $ J_n $. In our case, we prove that the Gr\"{o}bner fan contains a non-regular cone. We determine minimal generators of the initial ideal of $ J_n $ with respect to a certain monomial ordering, and show that the reduced Gr\"{o}bner basis of $ J_n $ has polynomials of certain forms for each $ n $.

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Rin Toh-Yama. 2018-04-30. Higher Nash Blowups of $A_3$-Singularity. https://arxiv.org/abs/1804.11050

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