Biman Roy

activity

20212026

collaborators

5 papers

math.AG2026

Rationality of varieties and $A^{1}$ -homotopy theory

Utsav Choudhury, Biman Roy

In this article, we present the results relating different rationality properties with $A^{1}$ -homotopy theoretic invariants.

math.AG2026

$A^{1}$ -fibration in algebraic geometry and $A^{1}$ -homotopy type

Utsav Choudhury, Aritra Mandal, Biman Roy

In this article we show that an $A^{1}$ bundle map or a vector bundle map $p : X \to Y$ induces trivial local fibration $S in g (X) \to S in g (Y)$ . Using t…

math.AG2026

Vector Bundles on Rational Topologically Contractible Affine Threefolds

Haoyang Liu, Biman Roy

The generalized Serre question asks whether every algebraic vector bundle on a topologically contractible smooth affine complex variety is trivial. We give an affirmative answer fo…

math.AG2024

$A^{1}$ -homotopy type of $A^{2} ∖ {(0, 0)}$

Utsav Choudhury, Biman Roy

In this article we prove that any $A^{1}$ -connected smooth $k$ -variety is $A^{1}$ -uniruled for any algebraically closed field $k$ . We establish that if a non empty op…

math.AG2021

$A^{1}$ -connected components and characterisation of $A^{2}$

Utsav Choudhury, Biman Roy

In this article we prove that any $A^{1}$ -contractible smooth complex surface is isomorphic as a variety to $C^{2}$ . We show that the $A^{1}$ -connected compone…

Rationality of varieties and A1-homotopy theory

A1-fibration in algebraic geometry and A1-homotopy type

Vector Bundles on Rational Topologically Contractible Affine Threefolds

A1-homotopy type of A2∖{(0,0)}

A1-connected components and characterisation of A2

Rationality of varieties and $A^{1}$ -homotopy theory

$A^{1}$ -fibration in algebraic geometry and $A^{1}$ -homotopy type

$A^{1}$ -homotopy type of $A^{2} ∖ {(0, 0)}$

$A^{1}$ -connected components and characterisation of $A^{2}$