arXiv subjects

Huy Tai Ha

Publications and source records attributed to Huy Tai Ha.

57 records · Page 4Linked to original sources

arXiv2002

The depth of the associated graded ring of ideals with any reduction number

Let R be a local Cohen-Macaulay ring, let I be an R-ideal, and let G be the associated graded ring of I. We give an estimate for the depth of G when G is not necessarily Cohen-Macaulay. We assume that I is either equimultiple, or has analytic deviation one, but we do not have any restriction on the reduction number. We also give a general estimate for the depth of G involving the first r+l powers of I, where r denotes the Castelnuovo regularity of G and l denotes the analytic spread of I.

math.AC↗

arXiv2002

Box-shaped matrices and the defining ideal of certain blowup surfaces

We study the defining equations of projective embeddings of the blowup of P^2 at a set of {d+1 \choose 2} number of points in generic position. To do this, we first generalize the notion of a matrix, its ideal of 2x2 minors to that of a box-shaped matrix. Our work completes previous works of Geramita and Gimigliano.

math.AC↗

arXiv2002

Arithmetic Macaulayfication of projective schemes

In this paper, we study arithmetic Macaulayfication of projective schemes and Rees algebras of ideals. We give a necessary and sufficient condition for a nonsingular projective scheme to have an arithmetic Macaulayfication. If the scheme is not necessarily nonsingular, we show that our condition give a sufficient condition for the existence of an arithmetic Macaulayfication. We also study truncated Rees algebra of an ideal. We show that the truncated Rees algebra R_λ(I) of an ideal I is alway Cohen-Macaulay for λlarge enough in some important situations.

math.AC↗