On the depth of graded rings associated to lex-segment ideals in $K[x,y]$ (2009)
In this article, we show that the depths of the associated graded ring and fiber cone of a lex-segment ideal in $K[x,y]$ are equal.
On the lengths of quotients of ideals and depths of fiber cones (2009)
Jayanthan, A. V., Nanduri, Ramakrishna
Let $(R,\mathfrak{m})$ be a Cohen-Macaulay local ring, $I$ an $\mathfrak{m}$-primary ideal of $R$ and $J$ its minimal reduction. We study the depths of $F(I)$ under certain depth assumptions on...
On the Koszul Betti numbers in positive characteristic (2008)
Jayanthan, A. V., Nanduri, Ramakrishna
We have observed a gap in one of the arguments in the main theorem. We choose to withdraw the paper until we rectify the gap.
Computational algebra and combinatorics of toric ideals (2008)
Diane Maclagan, Rekha R. Thomas, Sara Faridi, Leah Gold, A. V. Jayanthan, Amit Khetan, ...
Fiber cones of ideals with almost minimal multiplicity (2005)
Jayanthan, A. V., Verma, J. K.
Fiber cones of $0$-dimensional ideals with almost minimal multiplicity in Cohen-Macaulay local rings are studied. Ratliff-Rush closure of filtration of ideals with respect to another ideal is...
On fiber cones of ${\mathfrak m}$-primary ideals (2004)
Jayanthan, A. V., Puthenpurakal, Tony J., Verma, J. K.
Two formulas for the multiplicity of the fiber cone $F(I)=\oplus_{n=0}^{\infty} I^n/\m I^n$ of an $\m$-primary ideal of a $d$-dimensional Cohen-Macaulay local ring $(R,\m)$ are derived in terms of...
Graded rings associated with contracted ideals (2004)
Conca, Aldo, De Negri, Emanuela, Jayanthan, A. V., Rossi, Maria Evelina
By definition, an $\m$-primary ideal $I$ in a 2-dimensional regular local ring $(R, \m)$ is contracted if $I=R \cap IR[\m/x]$ for some $x \in \m \setminus \m^2$. Contracted ideals have been...
Fiber cones of ideals with almost minimal multiplicity (2002)
Jayanthan, A. V., Verma, J. K.
Fiber cones of 0-dimensional ideals with almost minimal multiplicity in Cohen-Macaulay local rings are studied. Ratliff-Rush closure of filtration of ideals with respect to another ideal is...
Local cohomology modules of bigraded Rees algebras (2002)
Jayanthan, A. V., Verma, J. K.
Formulas are obtained in terms of complete reductions for the bigraded components of local cohomology modules of bigraded Rees algebras of 0-dimensional ideals in 2-dimensional Cohen-Macaulay local...
Hilbert coefficients and depth of fiber cones (2002)
Jayanthan, A. V., Verma, J. K.
Criteria are given in terms of certain Hilbert coefficients for the fiber cone F(I) of an m-primary ideal I in a Cohen-Macaulay local ring (R,m) so that it is Cohen-Macaulay or has depth at least...
Hilbert coefficients and depths of form rings (2002)
Jayanthan, A. V., Singh, Balwant, Verma, J. K.
We present short and elementary proofs of two theorems of Huckaba and Marley, while generalizing them at the same time to the case of a module. The theorems concern a characterization of the depth of...
Grothendieck-Serre formula and bigraded Cohen-Macaulay Rees algebras (2002)
Jayanthan, A. V., Verma, J. K.
The Grothendieck-Serre formula for the difference between the Hilbert function and Hilbert polynomial of a graded algebra is generalized for bigraded standard algebras. This is used to get a similar...