arXiv subjects
Publications and source records attributed to Hoang Ngoc Yen.
This paper purposes to characterize Noetherian local rings $(R, \mathfrak{m})$ such that the Chern numbers of certain $\mathfrak{m}$-primary ideals in $R$ bounded above or range among only finitely many values. Consequently, we characterize the Gorensteinness, Cohen-Macaulayness, generalized Cohen-Macaulayness of local rings in terms of the behavior of its Chern numbers.
We explore the behavior of the sectional genera of certain primary ideals in Noetherian local rings. In this paper, we provide characterizations of a Cohen-Macaulay local ring in terms of the sectional genera, the Cohen-Macaulay type, and the second Hilbert coefficients for certain primary ideals. We also characterize Gorenstein rings and quasi-Buchsbaum rings in terms of the sectional genera for certain primary ideals.
In this paper, we give necessary and sufficient conditions for the existence of Ulrich bundles on cubic fourfold $X$ of given rank $r$. As consequences, we show that for every integer $r\ge 2$ there exists a family of indecomposable rank $r$ Ulrich bundles on the certain cubic fourfolds, depending roughly on $r$ parameters, and in particular they are of wild representation type; special surfaces on the cubic fourfolds are explicitly constructed by Macaulay2; a new $19$-dimensional family of projective ten-dimensional irreducible holomorphic symplectic manifolds associated to a certain cubic fourfold is constructed; and for certain cubic fourfold $X$, there exist arithmetically Cohen-Macaulay smooth surface $Y \subset X$ which are not an intersection $X \cap T$ for a codimension two subvariety $T \subset \Bbb P^5$.
In this paper, we explore the relation between the index of reducibility and the Hilbert coefficients in local rings. Consequently, the main result of this study provides a characterization of a sequentially Cohen-Macaulay ring in terms of its Hilbert coefficients for non-parameter ideals. As corollaries to the main theorem, we obtain characterizations of a Gorenstein/Cohen-Macaulay ring in terms of its Chern coefficients for parameter ideals.
In this paper, we explore a relationship between Hilbert functions and the irreducible decompositions of ideals in local rings. Applications are given to characterize the regularity, Gorensteinness, Cohen-Macaulayness and sequentially Cohen-Macaulayness of local rings.