A note on retracts of polynomial rings in three variables
classification
🧮 math.AG
keywords
fieldpolynomialaffirmativeansweraskscasecharacteristiccosta
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In Costa's paper published in 1977, he asks us whether every retract of $k^{[n]}$ is also the polynomial ring or not, where $k$ is a field. In this paper, we give an affirmative answer in the case where $k$ is a field of characteristic zero and $n = 3$.
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