Abstract: We discuss some problems related to the unboundedness of Betti numbers of families of affine curves defined by Numerical semigroups. We also indicate possible connections, with the help of examples, between the unboundedness of the last Betti number and the Cohen-Macaulayness of the projective closure of these affine curves. (Joint work with Ranjana Mehta, Joydip Saha & Pranjal Srivastav)
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