S OF SOME OF MY PAPERS GROUPED BY TOPIC 1. Regularity. Let k be an algebraically closed field. We will work over a standard graded polynomial ring U over k. Projective dimension and regularity are the main numerical invariants that measure the complexity of a minimal free resolution. Let L be a homogeneous ideal in U , and let b ij (L) be its graded Betti numbers. The projective dimension pd(L)...

Abstract In this paper, we study the Koszul property of homogeneous coordinate ring a generic collection lines in $\mathbb {P}^n$ and general linear position {P}^n.$ We show that if $\mathcal {M}$ is m with $2m \leq n+1$ R {M},$ then Koszul. Furthermore, even $m +1\leq n$ or odd +2\leq n,$ Lastly, such $$ \begin{align*} m> \frac{1}{72}\left(3(n^2+10n+13)+\sqrt{3(n-1)^3(3n+5)}\right),\end{ali...

The goal of the present paper is study some algebraic invariants Stanley–Reisner rings Cohen–Macaulay simplicial complexes dimension d−1. We prove that inequality d≤reg(Δ)⋅type(Δ) holds for any (d−1)-dimensional complex Δ satisfying Δ=core(Δ), where reg(Δ) (resp. type(Δ)) denotes Castelnuovo–Mumford regularity type) ring k[Δ]. Moreover, given integers d,r,t r,t≥2 and r≤d≤rt, we construct a Δ(G)...

In numerical algebraic geometry, a witness point set W is a key object for performing numerical computations on a projective scheme X of pure dimension d > 0 defined over C. If X is arithmetically Cohen-Macaulay, W can also be used to obtain information about X, such as the initial degree of the ideal generated by X and its Castelnuovo-Mumford regularity. Due to this relationship, we develop a ...

Let I be the defining ideal of a smooth irreducible complete intersection space curve C with defining equations of degrees a and b. We use the partial elimination ideals introduced by Mark Green to show that the lexicographic generic initial ideal of I has Castelnuovo-Mumford regularity 1+ ab(a− 1)(b− 1)/2 with the exception of the case a = b = 2, where the regularity is 4. Note that ab(a− 1)(b...

Suppose S is a parametrized surface in complex projective 3-space P given as the image of φ : P ×P1 → P. The implicitization problem is to compute an implicit equation F = 0 of S using the parametrization φ. An algorithm using syzygies exists for computing F if φ has no base points, i.e. φ is everywhere defined. This work is an extension of this algorithm to the case of a surface with multiple ...

Abstract We study the property of continuous Castelnuovo-Mumford regularity , for semihomogeneous vector bundles over a given Abelian variety, which was formulated in A. Küronya and Y. Mustopa [Adv. Geom. 20 (2020), no. 3, 401-412]. Our main result gives novel description thereof. It is expressed terms certain normalized polynomial functions that are obtained via Wedderburn decomposition variet...

We study monomial ideals with linear presentation or partially resolution. give combinatorial characterizations of for square-free degree 3, and primary whose resolutions are except the last step (the “almost linear” case). also sharp bounds on Castelnuovo–Mumford regularity numbers generators in some cases. It is a basic observation that linearity properties inherited by restriction an ideal t...