## Cohen-Macaulay Criteria for Projective Monomial Curves via Gröbner Bases

Published in Acta Mathematica Vietnamica

We prove new characterizations based on Gröbner bases for the Cohen-Macaulay property of a projective monomial curve.

Published in Acta Mathematica Vietnamica

We prove new characterizations based on Gröbner bases for the Cohen-Macaulay property of a projective monomial curve.

Published in Acta Mathematica Vietnamica

We give an account of recent works on Jacquet-Rallis’ approach to the Gan-Gross-Prasad conjecture for unitary groups. We report on the present state of the Jacquet-Rallis relative trace formulae and on some current applications of it. We give also a precise computation of the constant that appears in the statement “Fourier transform and transfer co...

Published in Acta Mathematica Vietnamica

Let (A,m)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(A,\mathfrak {m})$\end{document} be a Cohen-Macaulay local ring of dimension d and let I be an m\documentclass[1...

Published in Acta Mathematica Vietnamica

We describe the equations and Gröbner bases of some degenerate K3 surfaces associated to rational normal scrolls. These K3 surfaces are members of a class of interesting singular projective varieties we call correspondence scrolls. The ideals of these surfaces are nested in a simple way that allows us to analyze them inductively. We describe explic...

Published in Acta Mathematica Vietnamica

We present a close relationship between matching number, covering numbers and their fractional versions in combinatorial optimization and ordinary powers, integral closures of powers, and symbolic powers of monomial ideals. This relationship leads to several new results and problems on the containments between these powers.

Published in Acta Mathematica Vietnamica

Published in Acta Mathematica Vietnamica

Motivated by a conjecture of Huneke and Wiegand concerning torsion in tensor products of modules over local rings, we investigate the existence of ideals I in a one-dimensional Gorenstein local ring R satisfying ExtR1(I,I)=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage...

Published in Acta Mathematica Vietnamica

In this paper, we use polarization to study the behavior of the depth and regularity of a monomial ideal I, locally at a variable xi, when we lower the degree of all the highest powers of the variable xi occurring in the minimal generating set of I, and examine the depth and regularity of powers of edge ideals of clutters using combinatorial optimi...

Published in Acta Mathematica Vietnamica

Langlands’ functoriality principle predicts deep relations between the local and automorphic spectra of different reductive groups. This has been generalized by the relative Langlands program to include spherical varieties, among which reductive groups are special cases. In the philosophy of Langlands’ “beyond endoscopy” program, these relations sh...

Published in Acta Mathematica Vietnamica

In this paper, we give a formula for normal reduction number of an integrally closed m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathfrak m$\end{document}-primary ...