Algebraic variety is one of the most important subjects in the classical algebraic geometry. Algebraic variety in the classical algebraic geometry deals with the intersection of surfaces of polynomials.
It is well known that the face of any objects is combined by some surfaces, and their intersection, so to study the algebraic variety will be very important in both theory and practice.
Because of most surfaces have been recently represented in the piecewise polynomials, the study of so-called “Piecewise algebraic variety” defined as an intersection of surfaces represented by the piecewise polynomials should be also most important in both theory and practice.
In this talk, we will introduce some essentially difficulties in studying the piecewise algebraic variety, some results, and some open problems