A. V. Jayanthan

On fiber cones of m-primary ideals

Two formulas for the multiplicity of the fiber cone F(I) = L 1=0 I n/mIn of an m-primary ideal of a d-dimensional Cohen-Macaulay local ring (R, m) are derived in terms of the mixed mul- tiplicity ed 1(m|I), the multiplicity e(I), and superficial elements. As a consequence, the Cohen- Macaulay property of F(I) when I has minimal mixed multiplicity or almost minimal mixed multi- plicity is characterized in terms of the reduction number of I and lengths of certain ideals. We also characterize the Cohen-Macaulay and Gorenstein properties of fiber cones of m-primary ideals with a d-generated minimal reduction J satisfying l(I 2 / JI) = 1 or l(Im/ Jm) = 1.

Fiber cones of ideals with almost minimal multiplicity

Fiber cones of 0-dimensional ideals with almost minimal multiplicity in CohenMacaulay local rings are studied. Ratliff-Rush closure of filtration of ideals with respect to another ideal is introduced. This is used to find a bound on the reduction number with respect to an ideal. Rossi’s bound on reduction number in terms of Hilbert coefficients is obtained as a consequence. Sufficient conditions are provided for the fiber cone of 0-dimensional ideals to have almost maximal depth. Hilbert series of such fiber cones are also computed.

Grothendieck–Serre formula and bigraded Cohen–Macaulay Rees algebras

Abstract 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 formula for the difference between the Bhattacharya function and Bhattacharya polynomial of two m -primary ideals I and J in a local ring (A, m ) in terms of local cohomology modules of Rees algebras of I and J. The cohomology of a variation of the Kirby–Mehran complex for bigraded Rees algebras is studied which is used to characterize the Cohen–Macaulay property of bigraded Rees algebra of I and J for two dimensional Cohen–Macaulay local rings.

Periodic occurrence of complete intersection monomial curves

We study the complete intersection property of monomial curves in the family

Hilbert Coefficients and Depths of Form Rings

\Gamma_{\aa + \jj} = {(t^{a_0 + j}, t^{a_1+j},..., t^{a_n + j}) ~ | ~ j \geq 0, ~ a_0 < a_1 <...< a_n}

Castelnuovo–Mumford Regularity and Gorensteinness of Fiber Cone

. We prove that if

Local Cohomology Modules of Bigraded Rees Algebras

\Gamma_{\aa+\jj}

A Northcott type inequality for Buchsbaum-Rim coefficients

is a complete intersection for

On the Vasconcelos inequality for the fiber multiplicity of modules

j \gg0

Hilbert coefficients and depth of fiber cones

, then