论文标题
感谢您的品种和Gröbner基地：完整的Q-Factorial案例
Toric varieties and Gröbner bases: the complete Q-factorial case
论文作者
论文摘要
我们提出了两种算法，以确定所有完整和朴素的粉丝，他们承认固定的非脱位矢量$ v $作为其1型骨骼的发电机。这两种算法的相互作用使我们能够辨别相关的圆磨品种是否在任何维数和PICARD数值的值原理上接受了投射嵌入。第一种算法比第二个算法要慢，但是它计算出所有由$ V $支持的完整和简单风扇，并导致我们制定了关于风扇定义的拓扑组合猜想。 另一方面，我们将Sturmfels的论点适应了Gröbner的爱好者的粉丝，以适应我们的完整案例。我们给出了格布纳地区的特征，并显示了次级风扇的格布纳锥和腔室之间的明确对应关系。与$ v $相关的复的理想的均质化程序使我们能够使用GFAN和相关软件生成第二个算法。事实证明，后者比前者快得多，尽管它只能计算$ v $支持的投射粉丝。我们提供示例和开放问题列表。特别是，我们举例说明了$ \ q $的合理参数化家族的全曲面，以相反的方式相对于NEF锥体在特殊光纤上的尺寸跳跃。
We present two algorithms determining all the complete and simplicial fans admitting a fixed non-degenerate set of vectors $V$ as generators of their 1-skeleton. The interplay of the two algorithms allows us to discerning if the associated toric varieties admit a projective embedding, in principle for any values of dimension and Picard number. The first algorithm is slower than the second one, but it computes all complete and simplicial fans supported by $V$ and lead us to formulate a topological-combinatoric conjecture about the definition of a fan. On the other hand, we adapt the Sturmfels' arguments on the Gröbner fan of toric ideals to our complete case; we give a characterization of the Gröbner region and show an explicit correspondence between Gröbner cones and chambers of the secondary fan. A homogenization procedure of the toric ideal associated to $V$ allows us to employing GFAN and related software in producing our second algorithm. The latter turns out to be much faster than the former, although it can compute only the projective fans supported by $V$. We provide examples and a list of open problems. In particular we give examples of rationally parametrized families of $\Q$-factorial complete toric varieties behaving in opposite way with respect to the dimensional jump of the nef cone over a special fibre.
