Rational components of Hilbert schemes
Reduction of Power Series in a Polydisc with Respect to a Gröbner Basis
We deal with a reduction of power series convergent in a polydisc with respect to a Gröbner basis of a polynomial ideal. The results are applied to proving that a Nash function whose graph is algebraic in a "large enough" polydisc, must be a polynomial. Moreover, we give an effective method for finding this polydisc.
Regular Sequences of Symmetric Polynomials
Regularity for certain classes of monomial ideals.
Representations of non-negative polynomials via KKT ideals
This paper studies the representation of a non-negative polynomial f on a non-compact semi-algebraic set K modulo its KKT (Karush-Kuhn-Tucker) ideal. Under the assumption that f satisfies the boundary Hessian conditions (BHC) at each zero of f in K, we show that f can be represented as a sum of squares (SOS) of real polynomials modulo its KKT ideal if f ≥ 0 on K.
Résultats récents d'algèbre commutative effective