Parnashree Ghosh

activity

20222025

collaborators

11 papers

math.AC2025

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

Parnashree Ghosh

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

math.AG2025

Algebraic families of higher dimensional $A^{1}$ -contractible affine varieties non-isomorphic to affine spaces

Adrien Dubouloz, Parnashree Ghosh

We construct algebraic families of smooth affine $A^{1}$ -contractible varieties of every dimension $n \geq 4$ over fields of characteristic zero which are non-isomorphic to a…

math.AG2024

On embedding of linear hypersurfaces

Parnashree Ghosh, Neena Gupta, Ananya Pal

Linear hypersurfaces over a field $k$ have been playing a central role in the study of some of the challenging problems on affine spaces. Breakthroughs on such problems have occurr…

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.AG2024

On the family of affine threefolds $a (x) y = F (x, z, t)$

Parnashree Ghosh, Neena Gupta, Ananya Pal

In recent decades, linear affine threefolds have enabled researchers to solve some of the challenging problems on affine spaces. Koras-Russell threefolds, especially the Russell Cu…

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…

math.AC2022

On Generalised Danielewski and Asanuma varieties

Parnashree Ghosh, Neena Gupta

In this paper we extend a result of Dubouloz on the Cancellation Problem in higher dimensions ( $⩾ 2$ ) over the field of complex numbers to fields of arbitrary characteristi…

math.AC2022

On the triviality of a family of linear hyperplanes

Parnashree Ghosh, Neena Gupta

Let $k$ be a field, $m$ a positive integer, $V$ an affine subvariety of $A^{m + 3}$ defined by a linear relation of the form $x_{1}^{r_{1}}\cdots x_{m}^{r_{m}}y=F(x…

math.AC2022

A note on homogeneous rank $2$ locally nilpotent derivations on $k [X, Y, Z]$

Parnashree Ghosh

In this article we show that for every prime number $p$ , any irreducible homogeneous locally nilpotent derivations of rank $2$ and degree $p - 2$ are triangularizable. Further, we de…

math.AC2022

Some results on homogeneous locally nilpotent $R$ -derivations on $R [X, Y, Z]$

Parnashree Ghosh

Let $k$ be a field of characteristic zero and $R$ a $k$ -algebra. In this paper we study homogeneous $R$ -lnds $D$ on $R [X, Y, Z]$ with respect to the standard weights $(1, 1, 1)$ . We sh…

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

Algebraic families of higher dimensional A1-contractible affine varieties non-isomorphic to affine spaces

On embedding of linear hypersurfaces

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

On the family of affine threefolds a(x)y=F(x,z,t)

On characterization of Double Danielewski type algebras

On the triviality of an A2-fibration over a DVR

On Generalised Danielewski and Asanuma varieties

On the triviality of a family of linear hyperplanes

A note on homogeneous rank 2 locally nilpotent derivations on k[X,Y,Z]

Some results on homogeneous locally nilpotent R-derivations on R[X,Y,Z]

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

Algebraic families of higher dimensional $A^{1}$ -contractible affine varieties non-isomorphic to affine spaces

On the family of affine threefolds $a (x) y = F (x, z, t)$

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

A note on homogeneous rank $2$ locally nilpotent derivations on $k [X, Y, Z]$

Some results on homogeneous locally nilpotent $R$ -derivations on $R [X, Y, Z]$