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Publications


2014

  2014.  Vector Bundles of Low rank on a Multiprojective Space. Le Matematiche. Vol 69(No 2):pp31-41.Website

2013

Siro, L, Kamuti I.  2013.  On the Actions of the Symmetric Group, Sn, n ≤ 7 on Unordered Quadruples, X(4). International Journal of Algebra. Vol. 8, 2014(no. 3):115-120.

2012

  2012.  Monads on a multiprojective space. International Mathematical Forum. 7(53-54):2669-2673. AbstractLink

On this paper we define monads on projective spaces and extend them to multiprojective spaces with a view to constructing vector bundles of low rank in comparison to the dimension of the ambient space.

2011

Muindi, D.  2011.  The Minimal Resolution Conjecture for a dimension 4 projective space. Lambert Academic Publishing. (3843389373):64.
  2011.  Maximal rank for the Cotangent bundle over a general projective space.. International Mathematical Forum journal.. : Hikari Ltd Abstract

This is a generalization after my work on the projective space of dimension 4 to n.

Damian.  2011.  The Minimal Resolution Conjecture for an ideal of general points in a projective space. International Journal of Algebra. 4(9-12):477-500.: Hikari Ltd AbstractLink

The Minimal Resolution Conjecture (MRC) of Lorenzini predicts that the minimal free resolution of the homogeneous ideal I of S general points in a projective space of dimension n, contains no ghost terms, i.e. as predicted by Anna Lorenzini. I used the "la method d'Horace" to prove that a given evaluation map is of bijective and deduced maximal rank.

2010

  2010.  On the minimal number of generators of an Ideal of general points in a projective space, P4. ICM2010 Conference Proceedings. : 2010 Abstract

A short Communication presented at the ICM2010 in Hyderabad - India, on the 21st  of August 2010 .
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Charles Walter (Ed.).  2010.  Sur la conjecture de la minimale résolution de l’ideal d’un arrangement general d’un grand nombre de points dans un espace projectif. International Journal of Algebra. : Universite de Nice Sophia-Antipolis Abstract

The Minimal Resolution Conjecture is known and has been verified for Projective Spaces of dimension 2 and 3. Also there many counter examples for example for 11 points in a Projective Space of dimension 6, 12 points in a Projective Spaces of dimension 7. However, for Projective Spaces of dimension 4, it is believed to be true but the complete proof has not been written up so far. F Lauze tackled part of the resolution in his thesis.

2008

D, M.  2008.  On the Minimal Resolution Conjecture for P3. Internation Journal of Contemporary Mathematics. : Hikari Limited Abstract

The Minimal Resolution Conjecture is known to be true for projective spaces of dimension 2 and 3. In this article I used a variant method to prove it for P3.

2005

Maingi, D.  2005.  Groebner Basis over finite fields and over finite extensions of Q.. Internation Journal of Contemporary Mathematics. : Groebner-Bases-Bibliography-RICAM Abstract

The computation of Groebner Basis can be tedious and mid boggling. In this research we simplify the computation from any Field to Q-arithmetic which simplifies the algorithm even for computers.

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