定义非奇异环三维簇的理想的二次生成
Quadratic generation of ideals defining nonsigular toric 3-folds
AI总结：
针对两类非奇异环三维簇上的丰富线丛，证明其射影正规嵌入对应的理想可由二次元素生成。
AI中文摘要：
设X为非奇异环面上的射影线丛，该环面是射影平面沿至多4个不变点的爆破，或是射影直线乘积沿至多4个不变点的爆破。设L为X上的丰富线丛，则L将X定义为到大射影空间的射影正规嵌入。我们证明，该嵌入X的理想由二次元素生成。
英文摘要：
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.
