Moh's example of algebroid space curves

by Ranjana Mehta, Joydip Saha and Indranath Sengupt

Symmetric numerical semigroups formed by concatenation of arithmetic sequences

Given integer e?4, we have constructed a class of symmetric numerical semigroups of embedding dimension e and proved that the cardinality of a minimal presentation of the semigroup is a bounded function of the embedding dimension e. This generalizes the examples given by J.C. Rosales.by Ranjana Mehta, Joydip Saha and Indranath Sengupt

Frobenius number and minimal presentation of certain numerical semigroups

Suppose e≥4 be an integer, a=e+1, b>a+(e−3)d, gcd(a,d)=1 and d∤(b−a). Let M={a,a+d,a+2d,…,a+(e−3)d,b,b+d}, which forms a minimal generating set for the numerical semigroup Γe(M), generated by the set M. We calculate the Ap\'{e}ry set and the Frobenius number of Γe(M). We also show that the minimal number of generators for the defining ideal p of the affine monomial curve parametrized by X0=ta, X1=ta+d,…,Xe−3=ta+(e−3)d, Xe−2=tb, Xe−1=tb+d is a bounded function of e.Ranjana Mehta, Joydip Saha, and Indranath Sengupt

Betti numbers of Bresinsky's curves in A4

by Ranjana Mehta, Joydip Saha and Indranath Sengupt

Unboundedness of Betti numbers of curves

Bresinsky defined a class of monomial curves in A4 with the property that the minimal number of generators or the first Betti number of the defining ideal is unbounded above. We prove that the same behaviour of unboundedness is true for all the Betti numbers and construct an explicit minimal free resolution for this class. We also propose a general construction of such curves in arbitrary embedding dimension.by Ranjana Mehta, Joydip Saha and Indranath Sengupt