scholarly journals Initial sequences and Waldschmidt constants of planar point configurations

2017 ◽  
Vol 27 (06) ◽  
pp. 717-729 ◽  
Author(s):  
Łucja Farnik ◽  
J. Gwoździewicz ◽  
B. Hejmej ◽  
M. Lampa-Baczyńska ◽  
G. Malara ◽  
...  
Keyword(s):  
Planar Point ◽  
Symbolic Powers ◽  
Point Configurations ◽  
Waldschmidt Constants ◽  
Waldschmidt Constant

The purpose of this work is to extend the classification of planar point configurations with low Waldschmidt constants initiated in [M. Dumnicki, T. Szemberg and H. Tutaj-Gasińska, Symbolic powers of planar point configurations II, J. Pure Appl. Algebra 220 (2016) 2001–2016] and continued in [M. Mosakhani and H. Haghighi, On the configurations of points in [Formula: see text] with the Waldschmidt constant equal to two, J. Pure Appl. Algebra 220 (2016) 3821–3825] for all values less than [Formula: see text]. As a consequence, we prove a conjecture of Dumnicki, Szemberg and Tutaj-Gasińska concerning initial sequences with low first differences.

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 Symbolic powers of planar point configurations

2013 ◽  
Vol 217 (6) ◽  
pp. 1026-1036 ◽  
Author(s):  
M. Dumnicki ◽  
T. Szemberg ◽  
H. Tutaj-Gasińska
Keyword(s):  
Planar Point ◽  
Symbolic Powers ◽  
Point Configurations

scholarly journals Symbolic powers of planar point configurations II

2016 ◽  
Vol 220 (5) ◽  
pp. 2001-2016 ◽  
Author(s):  
M. Dumnicki ◽  
T. Szemberg ◽  
H. Tutaj-Gasińska
Keyword(s):  
Planar Point ◽  
Symbolic Powers ◽  
Point Configurations

scholarly journals Waldschmidt constants for Stanley–Reisner ideals of a class of simplicial complexes

2016 ◽  
Vol 15 (07) ◽  
pp. 1650137 ◽  
Author(s):  
Cristiano Bocci ◽  
Barbara Franci
Keyword(s):  
Simplicial Complexes ◽  
Combinatorial Approach ◽  
Ideal Formula ◽  
Symbolic Powers ◽  
Waldschmidt Constants ◽  
Waldschmidt Constant

We study the symbolic powers of the Stanley–Reisner ideal [Formula: see text] of a bipyramid [Formula: see text] over a [Formula: see text]-gon [Formula: see text]. Using a combinatorial approach, based on analysis of subtrees in [Formula: see text] we compute the Waldschmidt constant of [Formula: see text].

Einführung in eine anorganische Strukturchemie

1986 ◽  
Vol 175 (3-4) ◽  
Author(s):  
E. Hellner
Keyword(s):  
Three Dimensional ◽  
Standard Setting ◽  
Transformation Matrix ◽  
Two Dimensional ◽  
Coordination Polyhedra ◽  
Systematic Description ◽  
Point Configurations ◽  
Inorganic Structure

AbstractA systematic description and classification of inorganic structure types is proposed on the basis of homogeneous or heterogeneous point configurations (Bauverbände) described by invariant lattice complexes and coordination polyhedra; subscripts or matrices explain the transformation of the complexes in respect (M) to their standard setting; the value of the determinant of the transformation matrix defines the order of the complex. The Bauverbände (frameworks) may be described by three-dimensional networks or two-dimensional nets explicitely shown with structures types of the

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.

scholarly journals Symbolic powers in weighted oriented graphs

2021 ◽  
pp. 1-17
Author(s):  
Mousumi Mandal ◽  
Dipak Kumar Pradhan
Keyword(s):  
Oriented Graph ◽  
Explicit Description ◽  
Oriented Graphs ◽  
Edge Ideals ◽  
Underlying Graph ◽  
Symbolic Powers ◽  
Odd Cycle ◽  
Waldschmidt Constant

Let [Formula: see text] be a weighted oriented graph with the underlying graph [Formula: see text] when vertices with non-trivial weights are sinks and [Formula: see text] be the edge ideals corresponding to [Formula: see text] and [Formula: see text] respectively. We give an explicit description of the symbolic powers of [Formula: see text] using the concept of strong vertex covers. We show that the ordinary and symbolic powers of [Formula: see text] and [Formula: see text] behave in a similar way. We provide a description for symbolic powers and Waldschmidt constant of [Formula: see text] for certain classes of weighted oriented graphs. When [Formula: see text] is a weighted oriented odd cycle, we compute [Formula: see text] and prove [Formula: see text] and show that equality holds when there is only one vertex with non-trivial weight.

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