Kolloquien und Oberseminare Übersicht Detail

Vortragende Person/Vortragende Personen:
Austin Conner

When do a set of univariate polynomials have a common root? In the case of two polynomials, the classical Sylvester resultant answers this question, as it is a polynomial in the coefficients which vanishes exactly when there is a common root. For more than two polynomials, the set of equations vanishing on systems with a common root is no longer generated by one polynomial. In the special case where the polynomials in the set have the same degree, we determine the full ideal of equations. I will present this result and discuss its proof, which proceeds by ultimately showing the generators of the ideal form a Gröbner basis. This is accomplished indirectly by showing the variety generated by the leading monomials of the claimed equations is reduced and has the same dimension and degree as the variety whose equations we want.