4 papers
The Geometry of Locally Bounded Rational Functions
Victor Delage, Goulwen Fichou, Aftab Patel
This paper develops the geometry of locally bounded rational functions on non-singular real algebraic varieties. First various basic geometric and algebraic results regarding these…
Algebraic Approximation of Cohen-Macaulay Algebras
Aftab Patel
This paper shows that Cohen-Macaulay algebras can be algebraically approximated in such a way that their Cohen-Macaulayness and minimal Betti numbers are preserved. This is achieve…
Equisingular algebraic approximation of real and complex analytic germs
Janusz Adamus, Aftab Patel
We show that a Cohen-Macaulay analytic singularity can be arbitrarily closely approximated by germs of Nash sets which are also Cohen-Macaulay and share the same Hilbert-Samuel fun…
On finite determinacy of complete intersection singularities
Janusz Adamus, Aftab Patel
We give an elementary combinatorial proof of the following fact: Every real or complex analytic complete intersection germ X is equisingular -- in the sense of the Hilbert-Samuel f…