Antoni Rangachev

Antoni Rangachev
University of Chicago | UC · Department of Mathematics

PhD

About

20
Publications
1,860
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108
Citations
Introduction

Publications

Publications (20)
Preprint
Full-text available
Background: The COVID-19 pandemic followed a unique trajectory in Eastern Europe compared to other heavily affected regions, with most countries there only experiencing a major surge of cases and deaths towards the end of 2020 after a relatively uneventful first half of the year. However, the consequences of that surge have not received as much att...
Article
Full-text available
After initially having low levels of SARS-CoV-2 infections for much of the year, Bulgaria experienced a major epidemic surge at the end of 2020, which caused the highest recorded excess mortality in Europe, among the highest in the word (Excess Mortality Rate, or EMR ∼0.25%). Two more major waves followed in 2021, followed by another one in early 2...
Article
Full-text available
Background The COVID-19 pandemic has had a devastating impact on the world over the past two years (2020-2021). One of the key questions about its future trajectory is the protection from subsequent infections and disease conferred by a previous infection, as the SARS-CoV-2 virus belongs to the coronaviruses, a group of viruses the members of which...
Preprint
Full-text available
After initially having low levels of SARS-CoV-2 infections for much of the year, at the end of 2020 Bulgaria experienced a major epidemic surge, which caused the highest recorded excess mortality in Europe and among the highest in the word (Excess Mortality Rate, or EMR ~0.25%). Two more major waves followed in 2021, followed by another one in earl...
Article
Full-text available
The COVID-19 pandemic followed a unique trajectory in Eastern Europe compared to other heavily affected regions, with most countries there only experiencing a major surge of cases and deaths towards the end of 2020 after a relatively uneventful first half of the year. However, the consequences of that surge have not received as much attention as th...
Preprint
Full-text available
Background The COVID-19 pandemic has had a devastating impact on the world over the past two years (2020-2021). One of the key questions about its future trajectory is the protection from subsequent infections and disease conferred by a previous infection, as the SARS-CoV-2 virus belongs to the coronaviruses, a group of viruses the members of which...
Preprint
Full-text available
We introduce the restricted local volume of a relatively very ample invertible sheaf as an invariant of equisingularity by determining its change across families. We apply this result to give numerical control of Whitney-Thom (differential) equisingularity for families of isolated complex analytic singularities. The characterization of the vanishin...
Article
Full-text available
Let A be a Noetherian ring and B be a finitely generated A-algebra. Denote by A‾ the integral closure of A in B. We give necessary and sufficient conditions for prime ideals to be in AssA(B/A‾) and AssA‾(B/A‾) generalizing and strengthening classical results for rings of special type.
Preprint
Full-text available
Let A ⊂ B be integral domains. Suppose A is Noetherian and B is a finitely generated A-algebra. Denote by A' the integral closure of A in B. We show that A' is determined by finitely many unique discrete valuation rings. Our result generalizes Rees' classical valuation theorem for ideals. We also obtain a variant of Zariski's main theorem.
Article
Full-text available
We introduce a join construction as a way of completing the description of the relative conormal space of an analytic function on a complex analytic space that has a non-vanishing derivative at the origin. Then we show how to obtain a numerical criterion for Thom's A_f condition.
Preprint
Full-text available
Let A be a Noetherian ring and B be a finitely generated A-algebra. Denote by A' the integral closure of A in B. We give necessary and sufficient conditions for prime ideals to be in Ass_{A}(B/A') and Ass_{A'}(B/A') generalizing and strengthening classical results for rings of special type.
Preprint
We introduce a join construction as a way of completing the description of the relative conormal space of an analytic function on a complex analytic space that has a non-vanishing derivative at the origin. Then we show how to obtain a numerical criterion for Thom's A_f condition.
Article
Full-text available
Let $X:=\mathrm{Spec}(R)$ be an affine Noetherian scheme, and $\mathcal{M} \subset \mathcal{N}$ be a pair of finitely generated $R$-modules. Suppose either that $\mathcal{M}$ and $\mathcal{N}$ are locally free at the generic point of each irreducible component of $X$ or that the modules are contained in a free $R$-module. Let $\mathcal{M}^{n}$ and...
Article
Full-text available
We continue the development of the study of the equisingularity of isolated singularities, in the determinantal case. This version of the paper includes a substantial amount of new material (76% larger). The new material introduces the idea of the landscape of singularity, which includes the allowable deformations of the singularity and associated...
Article
Abstract This paper deals with some fundamental questions in the study of the diagonal diophan- tine equation a1x, s = 0over a finite extension K of the field Qp of p-adic numbers, namely some new upper bounds on the number of variables that ensure their solvability.

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