T. Syed

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20242026

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math.AG2026

Vector bundles over certain Koras-Russell threefolds of the third kind

Tariq Syed

Let $k$ be an algebraically closed base field of characteristic $0$ and let $I^\pm_{1}, I^\pm_{2}, I^\pm_{3}, d \geq 2$ be integers such that $I^\pm_{1}, I^\pm_{2}, I^\pm_{3}$ are pairwise coprime a…

math.AG2026

Efficient generation of projective modules: a motivic view

Aravind Asok, Morgan Opie, Brian Shin +1

Assume $k$ is a field and $R$ is a smooth $k$ -algebra of dimension $d$ . If $P$ is a projective module of rank $r$ , then it is well-known that $P$ can be generated by $r + d$ -elements…

math.AG2025

Motivic cohomology of cyclic coverings

Tariq Syed

Cyclic coverings produce many examples of topologically contractible smooth affine complex varieties. In this paper, we study the motivic cohomology groups of cyclic coverings over…

math.AG2025

On algebraic vector bundles of rank $2$ over smooth affine fourfolds

Thomas Brazelton, Morgan Opie, Tariq Syed

The classification of algebraic vector bundles of rank 2 over smooth affine fourfolds is a notoriously difficult problem. Isomorphism classes of such vector bundles are not uniquel…

math.AG2024

Some remarks on Spin-orbits of unit vectors

Tariq Syed

For $n \in N$ and a commutative ring $R$ with $2 \in R^{\times}$ , the group $S L_{n} (R)$ acts on the set $U m_{n} (R)$ of unimodular vectors of length $n$ and $S p i n_{2 n} (R)$ ac…

math.AG2024

Symplectic orbits of unimodular rows

Tariq Syed

For a smooth affine algebra $R$ of dimension $d \geq 3$ over a field $k$ and an invertible alternating matrix $I ¨ $ of rank $2 n$ , the group $S p (I ¨ )$ of invertible matrices of rank $…

Vector bundles over certain Koras-Russell threefolds of the third kind

Efficient generation of projective modules: a motivic view

Motivic cohomology of cyclic coverings

On algebraic vector bundles of rank 2 over smooth affine fourfolds

Some remarks on Spin-orbits of unit vectors

Symplectic orbits of unimodular rows

On algebraic vector bundles of rank $2$ over smooth affine fourfolds