发表机构
University of Ljubljana; Institute of Mathematics, Physics and Mechanics（卢布尔雅那大学; 数学、物理与力学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文构造仿射正规环面簇的显式平坦代数族，其完备化对所有等变变形万有，并证明约化基的不可约分支与切片多面体的极大格友好Minkowski分解双射对应，推广了已有定理。
AI 中文摘要
设$X_\sigma$为与全维强凸有理多面体锥$\sigma$相关联的仿射正规环面簇，并设$m$为具有切片$P_m=\sigma\cap[m=1]$的原始次数。我们构造了一个显式的平坦代数族，其完备化同时对所有次数$-jm$（$j\ge1$）的等变变形是万有的。我们证明了约化基的不可约分支与$P_m$的极大格友好Minkowski分解双射对应，并描述了每个分支上的诱导族。当$m\in\sigma^\vee$时，我们还获得了对$(X_\sigma,V(\chi^m))$的形式万有等变族。这些结果将先前的极小万有性和分支定理推广到任意仿射正规环面簇和任意原始次数。
英文摘要
Let $X_σ$ be the affine normal toric variety associated with a full-dimensional strongly convex rational polyhedral cone $σ$, and let $m$ be a primitive degree with slice $P_m=σ\cap[m=1]$. We construct an explicit flat algebraic family whose completion is universal for equivariant deformations in all degrees $-jm$, $j\ge1$, simultaneously. We prove that the irreducible components of the reduced base correspond bijectively to maximal lattice-friendly Minkowski decompositions of $P_m$, and describe the induced family on each component. When $m\inσ^\vee$, we also obtain a formally universal equivariant family for the pair $(X_σ,V(χ^m))$. These results extend earlier miniversality and component theorems to arbitrary affine normal toric varieties and arbitrary primitive degrees.
