Parnashree Ghosh

activity

20222025

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4 papers · 1 filter

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 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]

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

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