Geometric invariant theory for G a ⋊ G m $\mathbb {G}_a\rtimes \mathbb {G}_m$

IF 0.9 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-04-08 DOI:10.1112/blms.70065

Yikun Qiao

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Abstract

We study geometric invariant theory for $G_{a} ⋊_{d} G_{m}$ over characteristic zero. For a $G_{a} ⋊_{d} G_{m}$ -action on a variety $C$ in suitable case, we provide an equivariant birational modification $p : C^{'} \to C$ such that $C^{'} \to C^{'} / G_{a}$ is a principal bundle. The situation covers quotients of unstable strata of any linear ${SL}_{2}$ -action.

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G - a - G - m$ \mathbb {G}_a\r乘以\mathbb {G}_m$的几何不变量理论

我们研究了G a d G m$ \mathbb {G}_a\r乘以d\mathbb {G}_m$在特征零上的几何不变理论。在合适的情况下，对于G a d G m \mathbb {G}_a\ rx乘以d\mathbb {G}_m$ -作用于C$ C$，我们提供了一个等变双元修正p：C ‘→C$ p:C^{\ ’}\右C$使得C ‘→C ’ / G a$C^{\prime}\右row C^{\prime}/\mathbb {G}_a$是一个主束。这种情况涵盖了任意线性SL 2$ \ mathm {SL}_2$ -作用的不稳定层商。

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