waldschmidt constant
Recently Published Documents


TOTAL DOCUMENTS

16
(FIVE YEARS 2)

H-INDEX

3
(FIVE YEARS 0)

Author(s):  
Tu Chanh Nguyen ◽  
Dang Tuan Hiep

The paper shows values of the initial degree and Waldschmidt constant for some special cases including severalcases of ten points with three supporting lines in projective plane. These constants represent the complexity of optimal solutions in repeated path problems that have many applications in computer science, informatics theory and telecommunications.



Author(s):  
Mousumi Mandal ◽  
Dipak Kumar Pradhan

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.



Author(s):  
Tu Chanh Nguyen

We give a short survey about evaluation of initial degree and  Waldschmidt constant  of zero schemes  in projective space. We show main and updated results, some related conjectures and new computations of initial degree and Waldschmidt constant



Author(s):  
Edoardo Ballico ◽  
Giuseppe Favacchio ◽  
Elena Guardo ◽  
Lorenzo Milazzo

Abstract The aim of this paper is to make a connection between design theory and algebraic geometry/commutative algebra. In particular, given any Steiner System S(t, n, v) we associate two ideals, in a suitable polynomial ring, defining a Steiner configuration of points and its Complement. We focus on the latter, studying its homological invariants, such as Hilbert Function and Betti numbers. We also study symbolic and regular powers associated to the ideal defining a Complement of a Steiner configuration of points, finding its Waldschmidt constant, regularity, bounds on its resurgence and asymptotic resurgence. We also compute the parameters of linear codes associated to any Steiner configuration of points and its Complement.



2020 ◽  
Vol 224 (10) ◽  
pp. 106341 ◽  
Author(s):  
Maria Virginia Catalisano ◽  
Elena Guardo ◽  
Yong-Su Shin
Keyword(s):  


Author(s):  
Hassan Haghighi ◽  
Mohammad Mosakhani

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].



Author(s):  
Enrico Carlini ◽  
Huy Tài Hà ◽  
Brian Harbourne ◽  
Adam Van Tuyl




2019 ◽  
Vol 19 (10) ◽  
pp. 2050184
Author(s):  
Bidwan Chakraborty ◽  
Mousumi Mandal

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.



Author(s):  
Hassan Haghighi ◽  
Mohammad Mosakhani ◽  
Mohammad Zaman Fashami

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].



Sign in / Sign up

Export Citation Format

Share Document