Tame多项式的良好基

Functorial destackification of tame stacks with abelian stabilisers

We give an algorithm for removing stackiness from smooth, tame Artin stacks with abelian stabilisers by repeatedly applying stacky blow-ups. The construction works over a general base and is functorial with respect to base change and compositions with gerbes and smooth, stabiliser preserving maps. As applications, we indicate how the result can be used for destackifying general Deligne-Mumford stacks in characteristic zero, and to obtain a weak factorisation theorem for such stacks. Over an arbitrary field, the method can be used to obtain a functorial algorithm for desingularising varieties w…

关于驯顺自同构逼近、自同构群与 Ind-概形的增广拓扑，以及驯顺自同构群的自同构

On the tame authomorphism approximation, augmentation Topology of Automorphism Groups and $Ind$-schemes, and authomorphisms of tame automorphism groups

本文利用驯顺逼近研究多项式自同构 Ind-群的自同构，证明了 n≥3 时多项式代数自同构群的 Ind-概形自同构均为内自同构，并由此给出自同构群提升问题的否定解，进而探讨其与雅可比猜想的关系。

通过相交理论与商奇点研究基变换导子

Base change conductors through intersection theory and quotient singularities

本文利用相交理论与 Deligne 的 Riemann–Roch 定理，系统建立 Jacobian 基变换导子驯顺与野生部分的新计算方法，并分析弱野生商奇点下的潜在好约化。

Entanglement of four-qubit systems: a geometric atlas with polynomial compass II (the tame world)

We propose a new approach to the geometry of the four-qubit entanglement classes depending on parameters. More precisely, we use invariant theory and algebraic geometry to describe various stratifications of the Hilbert space by SLOCC invariant algebraic varieties. The normal forms of the four-qubit classification of Verstraete {\em et al.} are interpreted as dense subsets of components of the dual variety of the set of separable states and an algorithm based on the invariants/covariants of the four-qubit quantum states is proposed to identify a state with a SLOCC equivalent normal form (up to…

Canonical bases for the quantum extended Kac-Moody algebras and Hall polynomials

In this paper, the singular Ringel-Hall algebra for a tame quiver is introduced and shown to be isomorphic to the positive part of the quantum extended Kac-Moody algebra. A PBW basis is constructed and a new class of perverse sheaves is shown to have purity property. This allows to construct the canonical bases of the positive part of the quantum extended Kac-Moody algebra. As an application, the existence of Hall polynomials for tame quiver algebras is proved.