Talker: Gábor Bodnár
The resolution algorithm requires performing blowing ups along nontrivial centers. The operation of blowing up is well known for arbitrary centers, but it is a very cumbersome process, requiring Gröbner basis computation with lexdeg ordering in more variables than the generators of the polynomial ring. We have to apply blowing ups repeatedly in the resolution, so the general solution is not viable in this environment. We rather restrict the blowing up centers to arise as intersections of hypersurfaces that give rise to regular systems of parameters in every point of the ambient smooth variety. With this approach the blowing ups need more careful preparation, but eventually the operation turns out to be very efficiently computable.
In this talk we describe the the representation of charts, and both the blowing up operation and the operations needed to prepare blowing ups (cover, exchange).
