arXiv subjects

Muhammad Imran Qureshi

Publications and source records attributed to Muhammad Imran Qureshi.

25 records · Page 2Linked to original sources

arXiv2014

Constructing projective varieties in weighted flag varieties II

We give the construction of weighted Lagranngiann Grassmannians$wLGr(3,6)$ and weighted partial $A_3$ flag variety $wFl_{1,3}$ coming from the symplectic Lie group $Sp(6,\mathbb C)$ and the general linear group $GL(4,\mathbb C)$ respectively. We give general formulas for their Hilbert series in terms of Lie theoretic data. We use them as key varieties (Format) to construct some families of polarized 3-folds in codimension 7 and 9. At the end, we list all the distinct weighted flag varieties in codimension $4\le c\le 10$.

math.AG↗

arXiv2012

Stanley depth and complete $k$-partite hypergraphs

We give an upper bound for the Stanley depth of the edge ideal of a complete $k$-partite hypergraph and as an application we give an upper bound for the Stanley depth of a monomial ideal in a polynomial ring $S$. We also give a lower and an upper bound for the cyclic module $S/I$ associated to the complete $k$-partite hypergraph.

math.AC↗

arXiv2011

Calabi-Yau threefolds in weighted flag varieties

We review the construction of families of projective varieties, in particular Calabi--Yau threefolds, as quasilinear sections in weighted flag varieties. We also describe a construction of tautological orbi-bundles on these varieties, which may be of interest in heterotic model building.

math.AG↗

arXiv2011

Stanley depth of edge ideals

We give an upper bound for the Stanley depth of the edge ideal $I$ of a $k$-partite complete graph and show that Stanley's conjecture holds for $I$. Also we give an upper bound for the Stanley depth of the edge ideal of a $k$-uniform complete bipartite hypergraph.

math.AC↗

arXiv2010

Constructing projective varieties in weighted flag varieties

We compute the Hilbert series of general weighted flag varieties and discuss a computer-aided method to determine their defining equations. We apply our results to weighted flag varieties coming from the Lie groups of type G_2 and GL(6), to construct some families of polarised projective varieties in codimensions 8 and 6, respectively.

math.AG↗

arXiv2010

On the Behaviour of Stanley Depth under Variable Adjunction

Let $S=K[x_1,...,x_n]$ be a polynomial ring in $n$ variables over the field $K$. For integers $1\leq t< n$ consider the ideal $I=(x_1,...,x_t)\cap(x_{t+1}, ...,x_n)$ in $S$. In this paper we bound from above the Stanley depth of the ideal $I'=(I,x_{n+1},...,x_{n+p})\subset S'=S[x_{n+1},...,x_{n+p}]$. We give similar upper bounds for the Stanley depth of the ideal $(I_{n,2},x_{n+1},...,x_{n+p})$, where $I_{n,2}$ is the square free Veronese ideal of degree 2 in $n$ variables.

math.AC↗

arXiv2009

Computing the Stanley depth

Let $Q$ and $Q'$ be two monomial primary ideals of a polynomial algebra $S$ over a field. We give an upper bound for the Stanley depth of $S/(Q\cap Q')$ which is reached if $Q$,$Q'$ are irreducible. Also we show that Stanley's Conjecture holds for $Q_1\cap Q_2$, $S/(Q_1\cap Q_2\cap Q_3)$, $(Q_i)_i$ being some irreducible monomial ideals of $S$.

math.AC↗