A numerical criterion for simultaneous normalization

Simultaneous normalization and algebra husks

The aim of this note is to use the concept of algebra husks to prove an analog of the flattening decomposition theorem for simultaneous normalizations. Other applications improve earlier flatness criteria. Parts of this note were contained in the first version of "Hulls and Husks" (arXiv:0805.0576). Dec. 16: new references added.

Rational Homology Manifolds and Hypersurface Normalizations

We prove a criterion for determining whether the normalization of a complex analytic space on which the constant sheaf is perverse is a rational homology manifold, using a perverse sheaf known as the multiple-point complex. This perverse sheaf is naturally associated to any "parameterized space", and has several interesting connections with the Milnor monodromy and mixed Hodge Modules.

模空间上周期映射和仿射结构的同时归一化

Simultaneous normalization of period map and affine structures on moduli spaces

本文证明了模空间上周期映射与仿射结构的同时归一化，并展示了极化 manifold 的Teichmüller空间具有复仿射结构。

Trace ideals, normalization chains, and endomorphism rings

In this paper we consider reduced (non-normal) commutative noetherian rings $R$. With the help of conductor ideals and trace ideals of certain $R$-modules we deduce a criterion for a reflexive $R$-module to be closed under multiplication with scalars in an integral extension of $R$. Using results of Greuel and Knörrer this yields a characterization of plane curves of finite Cohen--Macaulay type in terms of trace ideals. Further, we study one-dimensional local rings $(R,\mathfrak{m})$ such that that their normalization is isomorphic to the endomorphism ring $\mathrm{End}_R(\mathfrak{m})$: we gi…

delta不变量与孤立非正常奇点的同时规范化

The Delta Invariant and Simultaneous Normalization for Families of Isolated Non-Normal Singularities

本文研究了孤立非正常奇点的delta不变量及其在族中的上半连续性，提出在纤维上可规范化的条件，并推广了经典结果。

Explicit Noether Normalization for Simultaneous Conjugation via Polynomial Identity Testing

Mulmuley recently gave an explicit version of Noether's Normalization lemma for ring of invariants of matrices under simultaneous conjugation, under the conjecture that there are deterministic black-box algorithms for polynomial identity testing (PIT). He argued that this gives evidence that constructing such algorithms for PIT is beyond current techniques. In this work, we show this is not the case. That is, we improve Mulmuley's reduction and correspondingly weaken the conjecture regarding PIT needed to give explicit Noether Normalization. We then observe that the weaker conjecture has recen…