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arXiv · 2608.19577

Quadratic generation of ideals defining nonsigular toric 3-folds

Shoetsu Ogata
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Abstract

Let $X$ be a projective line bundle over a nonsingular toric surface which is a blowup the projective plane along at most 4 invariant points, or a blowup the product of the projective lines along at most 4 invariant points. Let $L$ be an ample line bundle on $X$. Then $L$ defines a projectively normal embedding to big projective space. We show the ideal of this embedded $X$ is generated by elements of degree two.

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Shoetsu Ogata. 2026-08-20. Quadratic generation of ideals defining nonsigular toric 3-folds. https://arxiv.org/abs/2608.19577

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