Geometric Fiber Classification
Published:
This project provides an algorithm to classify geometric fibers by their cardinality. Roughly speaking, if $f_1(u,x)=\cdots=f_s(u,x)=0, h(u,x)\ne 0$ is a polynomial system in parameters $u$ and unknowns $x$, the goal is to find the conditions on $u$ such that the system has exactly $d$ distinct (complex) solutions in $x$, where $d\in [0,+\infty]$ ($+\infty$ means there are infinitely many solutions).