All Fat Point Subschemes in $${\mathbb {P}}^2$$ with the Waldschmidt Constant Less than 5 / 2

2019 ◽  
Vol 43 (4) ◽  
pp. 3221-3228
Author(s):  
Hassan Haghighi ◽  
Mohammad Mosakhani
Keyword(s):  
Fat Point ◽  
Waldschmidt Constant

scholarly journals Resurgence and Waldschmidt constant of the ideal of a fat almost collinear subscheme in ℙ2

2018 ◽  
Vol 17 (1) ◽  
pp. 59-65 ◽  
Author(s):  
Hassan Haghighi ◽  
Mohammad Mosakhani ◽  
Mohammad Zaman Fashami
Keyword(s):  
Homogeneous Ideal ◽  
Fat Point ◽  
Waldschmidt Constant ◽  
The Ideal

Abstract Let Zn = p0 + p1 + ··· + pn be a configuration of points in ℙ2, where all points pi except p0 lie on a line, and let I(Zn) be its corresponding homogeneous ideal in 𝕂 [ℙ2]. The resurgence and the Waldschmidt constant of I(Zn) in [5] have been computed. In this note, we compute these two invariants for the defining ideal of a fat point subscheme Zn,c = cp0 + p1 +··· + pn, i.e. the point p0 is considered with multiplicity c. Our strategy is similar to [5].

Kähler Differentials for Fat Point Schemes in ℙ1×ℙ1

2021 ◽  
Vol 13 (2) ◽  
Author(s):  
Elena Guardo ◽  
Martin Kreuzer ◽  
Tran N. K. Linh ◽  
Le Ngoc Long
Keyword(s):  
Fat Point ◽  
Kähler Differentials

scholarly journals Fat point embeddings in affine space

2008 ◽  
Vol 212 (7) ◽  
pp. 1583-1593
Author(s):  
Jean-Philippe Furter
Keyword(s):  
Affine Space ◽  
Fat Point

Fat Points in ℙ1× ℙ1and Their Hilbert Functions

2004 ◽  
Vol 56 (4) ◽  
pp. 716-741 ◽  
Author(s):  
Elena Guardo ◽  
Adam Van Tuyl
Keyword(s):  
Finite Number ◽  
Hilbert Function ◽  
Free Resolution ◽  
Hilbert Functions ◽  
Minimal Free Resolution ◽  
Fat Points ◽  
Fat Point ◽  
Point Scheme

AbstractWe study the Hilbert functions of fat points in ℙ1× ℙ1. IfZ⊆ ℙ1× ℙ1is an arbitrary fat point scheme, then it can be shown that for everyiandjthe values of the Hilbert functionHZ(l,j) andHZ(i,l) eventually become constant forl≫ 0. We show how to determine these eventual values by using only the multiplicities of the points, and the relative positions of the points in ℙ1× ℙ1. This enables us to compute all but a finite number values ofHZwithout using the coordinates of points. We also characterize the ACM fat point schemes using our description of the eventual behaviour. In fact, in the case thatZ⊆ ℙ1× ℙ1is ACM, then the entire Hilbert function and its minimal free resolution depend solely on knowing the eventual values of the Hilbert function.

scholarly journals The Waldschmidt constant for squarefree monomial ideals

2016 ◽  
Vol 44 (4) ◽  
pp. 875-904 ◽  
Author(s):  
Cristiano Bocci ◽  
Susan Cooper ◽  
Elena Guardo ◽  
Brian Harbourne ◽  
Mike Janssen ◽  
...  
Keyword(s):  
Monomial Ideals ◽  
Waldschmidt Constant

On the configurations of codimension two linear subspaces of ℙN with the Waldschmidt constant less than 2

2020 ◽  
pp. 2150178
Author(s):  
Hassan Haghighi ◽  
Mohammad Mosakhani
Keyword(s):  
Hilbert Function ◽  
Free Resolution ◽  
Minimal Free Resolution ◽  
Codimension Two ◽  
Symbolic Powers ◽  
Point Configurations ◽  
Higher Dimensional ◽  
Algebraic Invariants ◽  
Waldschmidt Constants ◽  
Waldschmidt Constant

The purpose of this note is to generalize a result of [M. Dumnicki, T. Szemberg and H. Tutaj-Gasińska, Symbolic powers of planar point configurations II, J. Pure Appl. Alg. 220 (2016) 2001–2016] to higher-dimensional projective spaces and classify all configurations of [Formula: see text]-planes [Formula: see text] in [Formula: see text] with the Waldschmidt constants less than two. We also determine some numerical and algebraic invariants of the defining ideals [Formula: see text] of these classes of configurations, i.e. the resurgence, the minimal free resolution and the regularity of [Formula: see text], as well as the Hilbert function of [Formula: see text].

scholarly journals Invariants of the symbolic powers of edge ideals

2019 ◽  
Vol 19 (10) ◽  
pp. 2050184
Author(s):  
Bidwan Chakraborty ◽  
Mousumi Mandal
Keyword(s):  
Complete Graph ◽  
Explicit Description ◽  
Edge Ideal ◽  
Edge Ideals ◽  
Single Vertex ◽  
Symbolic Powers ◽  
Odd Cycles ◽  
Waldschmidt Constant

Let [Formula: see text] be a graph and [Formula: see text] be its edge ideal. When [Formula: see text] is the clique sum of two different length odd cycles joined at single vertex then we give an explicit description of the symbolic powers of [Formula: see text] and compute the Waldschmidt constant. When [Formula: see text] is complete graph then we describe the generators of the symbolic powers of [Formula: see text] and compute the Waldschmidt constant and the resurgence of [Formula: see text]. Moreover for complete graph we prove that the Castelnuovo–Mumford regularity of the symbolic powers and ordinary powers of the edge ideal coincide.

On the configurations of points in P2 with the Waldschmidt constant equal to two

2016 ◽  
Vol 220 (12) ◽  
pp. 3821-3825 ◽  
Author(s):  
Mohammad Mosakhani ◽  
Hassan Haghighi
Keyword(s):  
Waldschmidt Constant
Sign in / Sign up

Export Citation Format

Share Document