Biman Roy

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20212026

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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…

Rationality of varieties and A1-homotopy theory

A1-fibration in algebraic geometry and A1-homotopy type

Vector Bundles on Rational Topologically Contractible Affine Threefolds

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

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