11 citations · 23 across the 10 of their papers we have counts for
13 papers
On the triviality of an -fibration over a DVR
Parnashree Ghosh, Neena Gupta
In this paper we show that any -fibration over a discrete valuation ring which is also an -form is necessarily a polynomial ring. Further we show that s…
The Zariski Cancellation Problem and related problems in Affine Algebraic Geometry
Neena Gupta
In this article, we shall discuss the solution to the Zariski Cancellation Problem in positive characteristic, various approaches taken so far towards the possible solution in char…
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 () over the field of complex numbers to fields of arbitrary characteristi…
On the triviality of a family of linear hyperplanes
Parnashree Ghosh, Neena Gupta
Let be a field, a positive integer, an affine subvariety of defined by a linear relation of the form $x_{1}^{r_{1}}\cdots x_{m}^{r_{m}}y=F(x…
On finite generation of Noetherian algebras over two-dimensional regular local rings
Amartya Kumar Dutta, Neena Gupta, Nobuharu Onoda
Let be a complete regular local ring with an algebraically closed residue field and let be a Noetherian -subalgebra of the polynomial ring . It has been shown in \…
Some results on retracts of polynomial rings
Sagnik Chakraborty, Nikhilesh Dasgupta, Amartya Kumar Dutta +1
In this paper, we first consider the relationship between a polynomial ring over a Noetherian domain and the ring of invariants of a -action on , when…
On Double Danielewski Surfaces and the Cancellation Problem
Neena Gupta, Sourav Sen
We study a two-dimensional family of affine surfaces which are counter-examples to the Cancellation Problem. We describe the Makar-Limanov invariant of these surfaces, determine th…
On Separable $\A^2$ and $\A^3$-forms
Amartya Kumar Dutta, Neena Gupta, Animesh Lahiri
In this paper, we will prove that any $\A^3$-form over a field of characteristic zero is trivial provided it has a locally nilpotent derivation satisfying certain properties. W…
An algebraic characterization of the affine three space
Nikhilesh Dasgupta, Neena Gupta
In this paper we give algebraic characterizations of the affine -space and the affine -space over an algebraically closed field of characteristic zero, using a variant of the…
Nice derivations over principal ideal domains
Nikhilesh Dasgupta, Neena Gupta
In this paper we investigate to what extent the results of Z. Wang and D. Daigle on nice derivations of the polynomial ring in three variables over a field k of characteristic zero…
Some K-theoretic properties of the kernel of a locally nilpotent derivation on k[X_1, \dots, X_4]
S. M. Bhatwadekar, Neena Gupta, Swapnil A. Lokhande
Let k be an algebraically closed field of characteristic zero, D a locally nilpotent derivation on the polynomial ring k[X_1, X_2,X_3,X_4] and A the kernel of D. A question of M. M…
On Zariski's Cancellation Problem in positive characteristic
Neena Gupta
In this paper we shall show that when k is a field of positive characteristic the affine space A^n_k is not cancellative for any n greater than 2.
A Counter-example to the Cancellation Problem for the Affine Space A^3 in characteristic p
Neena Gupta
We show that the Cancellation Conjecture does not hold for the affine space A^3_k over any field k of positive characteristic. We prove that an example of T. Asanuma provides a thr…