SEMIGROUP OF ORDINARY MULTIPLE POINT, ANALYSIS OF STRAIGHTENING FORMULA AND COUNTING MONOMIALS (DETAIL IDEAL LADDER)
Abstract
In the first chapter we define the semigroup of ordinary multiple point of an analytic plane curve f and give its characterisation. The structure of this semigroup is completely decided by the order of f. In the second chapter we give a detailed analysis of the straightening formula given by Rota. Among other things we give an algorithm to straighten a nonstandard pure unitableau of depth 2 using any violation. In the third chapter we count certain subset of monomials of degree V in a ladder type array of indeterminates. We give a formula counting monomials in a ladder type array of indeterminates of degree V and of index (LESSTHEQ)1 and show that it is a polynomial in V with rational coefficients. Using Abhyankar's theorem, we deduce that the ideal generated by 2 x 2 minors of the ladder-type array of indeterminates in the corresponding polynomial ring is Hilbertian i.e. the Hilbert polynomial of the ideal coincides with its Hilbert function for all nonnegative integers.
Degree
Ph.D.
Subject Area
Mathematics
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