A. V. Jayanthan's home page

My research interests lie in the area of Commutative Algebra. My thesis was on problems related to the homological properties of the blowup algebras. I did Ph.D. under the guidance of Prof. Jugal K. Verma at the Department of Mathematics, IIT Bombay on The Hilbert coefficients and depth of Blowup algebras.

I continued doing research on blowup algebras for a while. I also studied a generalization of Hilbert-Samuel function and polynomials to the case of modules, known as Buchsbaum-Rim function, the corresponding polynomial and its coefficients. Of late, I am more interested in combinatorial commutative algebra. The aim is to understand the interplay between the combinatorial invariants associated to a graph and the algebraic invariants associated to monomial and binomial edge ideals.

Publications / Preprints :

Subadditivity, strand connectivity and multigraded Betti numbers of monomial ideals, J. Commut. Algebra 15 (2023), no. 4, 519–541., with Arvind Kumar.
Binomial expansion for saturated and symbolic powers of sums of ideals, J. Algebra 620 (2023), 690–710., with Huy Tai Ha, Arvind Kumar and Nguyen D. Hop.
On the resurgence and asymptotic resurgence of homogeneous ideals, Math. Z. 302 (2022), no. 4, 2407–2434., with Arvind Kumar and Vivek Mukundan
Bound for the regularity of binomial edge ideals of cactus graphs, Algebra Colloquium 29 (2022) no. 3, 443-452., with Rajib Sarkar
Resurgence numbers of fiber products of projective schemes, Collect. Math. 72 (2021), no. 1, 605-615, with Sankhaneel Bisui, Huy Tai Ha and Abu Chackalamannil Thomas.
Linear polynomial for the regularity of powers of edge ideals of very well-covered graphs J. Commut. Algebra 13 (2021), no. 1, 89-101 , with S. Selvaraja.
Upper bounds for the regularity of powers of edge ideals of graphs, J. Algebra 574 (2021), 184-205, with S. Selvaraja.
Almost complete intersection binomial edge ideals and their Rees algebras Journal of Pure and Applied Algebra, 225(6) (2021), 106628, with Arvind Kumar and Rajib Sarkar.
Regularity of powers of quadratic sequences with applications to binomial ideals J. Algebra, 564 (2020), 98-118, with Arvind Kumar and Rajib Sarkar
Regularity of Symbolic Powers of Edge Ideals J. Pure Appl. Algebra 224 (2020), no. 7, 106306, 12 pp. with Rajiv Kumar.
Regularity of binomial edge ideals of Cohen-Macaulay bipartite graphs , Comm. Algebra 47 (2019), no. 11, 4797-4805, with Arvind Kumar.
An upper bound for the regularity of binomial edge ideals of trees J. Algebra Appl. 18 (2019) no. 9, 1950170, 7pp, with N. Narayanan and B. V. Raghavendra Rao.
Syzygies, Betti numbers and regularity of cover ideals of certain multipartite graphs Mathematics, (2019) 7(9), 869, with Neeraj Kumar.
On the Vasconcelos inequality for the fiber multiplicity of modules Comm. Algebra 46 (2018), 3322 - 3333, with R. Balakrishnan.
Regularity of binomial edge ideals of certain block graphs, Proc. Indian Acad. Sci. Math. Sci. 129 (2019), no. 3, Art. 36, 10 pp , with N. Narayayan and B. V. Raghavendra Rao.
Regularity of powers of bipartite graphs, J. Algebraic Combin. 47 no. 1, (2018), 17 - 38, with N. Narayanan and S. Selvaraja
A Northcott type inequality for Buchsbaum-Rim coefficients, J. Commut. Algebra, 8 (2016), no. 4, 493 - 512. (with R. Balakrishnan)
On the number of generators of ideals defining Gorenstein Artin algebras with Hilbert function $(1,n+1 , 1+{n+1\choose 2}, \ldots,{n+1\choose 2}+1, n+1 ,1)$ Beiträge Algebra Geom. 57 (2016), no. 1, 173 - 187. (with Sabine El Khoury and Hema Srinivasan).
On the relation type of fiber cone, Acta Math. Viet., 40 (2015) no. 3, 535-544. (with Ramakrishna Nanduri)
On the depth of fiber cones of stretched $\mathfrak{m}$-primary ideals Indian J. Pure Appl. Math. 45 (2014), no. 6, 925 - 942. (with Ramakrishna Nanduri)
Periodic Occurrence of Complete Intersection Monomial Curves, Proc. Amer. Math. Soc. 141 (2013), no. 12, 4199-4208. (with Hema Srinivasan).
Castelnuovo-Mumford Regularity and Gorensteinness of fiber cone Comm. Algebra 40 (2012), no. 4, 1338-1351.
On the depth of graded rings associated to lex-segment ideals in $k[x,y]$, Beiträge Algebra Geom. 51 (2010), no. 1, 147-153.
On fiber cones of $\mathfrak{m}$-primary ideals, Canadian J. Math., 59 (2007) no. 1 109-126. (with Tony J. Puthenpurakal and J. K. Verma).
Graded rings associated with contracted ideals, J. Algebra, 284 (2005) 593-626. (with A. Conca, E. DeNegri and M. E. Rossi).
Fiber cones of ideals with almost minimal multiplicity, Nagoya Math. J., 177 (2005) 155-179. (with J. K. Verma)
Hilbert coefficients and depth of fiber cone, J. Pure Appl. Algebra, 201 (2005) 97-115. (with J. K. Verma)
Hilbert Coefficients and Depths of Form Rings, Comm. Algebra, 32 (2004) no.4, 1445-1452. (with J. K. Verma and Balwant Singh)
Local cohomology of bigraded Rees algebras, Advances in Algebra and Geometry (Hyderabad, 2001), 39-52, Hindustan Book Agency, New Delhi, 2003. (with J. K. Verma)
Grothendieck-Serre Formula and Bigraded Cohen-Macaulay Rees Algebras, J. Algebra, 254 no. 1 (2002), 1-20 (with J. K. Verma)