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arXiv · 2409.03985

The Syzygy Matrix and the Differential for Rational Curves in Projective Space

Chen Song
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Abstract

In this paper, we study whether a given morphism $f$ from the tangent bundle of $\mathbb{P}^1$ to a balanced vector bundle of degree $(n+1)d$ is induced by the restriction of the tangent bundle $T_{\mathbb{P}^n}$ to a rational curve of degree $d$ in $\mathbb{P}^n$. We propose a conjecture on this problem based on Mathematica computations of some examples and provide computer-assisted proof of the conjecture for certain values of $n$ and $d$.

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Chen Song. 2024-09-06. The Syzygy Matrix and the Differential for Rational Curves in Projective Space. https://arxiv.org/abs/2409.03985

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