Parnashree Ghosh

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math.AC2025

On $A^{1}$ -contractibility of certain simple birational extensions of affine spaces

Parnashree Ghosh

Over a field of characteristic zero, up to isomorphism of varieties, affine spaces are the only smooth $A^{1}$ -contractible affine varieties in dimensions $⩽ 2$ . How…

math.AC2024

A new family of counterexamples to the Zariski Cancellation Problem in positive characteristic

Parnashree Ghosh, Ananya Pal

In this paper, over a field of positive characteristic we exhibit an infinite family of counter examples to the Zariski Cancellation Problem in higher dimensions ( $⩾ 3$ ) wh…

math.AC2024

On characterization of Double Danielewski type algebras

Parnashree Ghosh, Dibyendu Mondal

Let $k$ be a field. In this paper, we consider Double Danielewski type algebras over an affine factorial $k$ -domain $R$ . We observe that this family produces a non-cancellative fam…

math.AC2023

On the triviality of an $A^{2}$ -fibration over a DVR

Parnashree Ghosh, Neena Gupta

In this paper we show that any $A^{2}$ -fibration over a discrete valuation ring which is also an $A^{2}$ -form is necessarily a polynomial ring. Further we show that s…

On A1-contractibility of certain simple birational extensions of affine spaces

A new family of counterexamples to the Zariski Cancellation Problem in positive characteristic

On characterization of Double Danielewski type algebras

On the triviality of an A2-fibration over a DVR

On $A^{1}$ -contractibility of certain simple birational extensions of affine spaces

On the triviality of an $A^{2}$ -fibration over a DVR