Some applications of computer algebra to vector bundles on projective spaces

During the past years the results and the techniques of computer algebra have become more and more useful in algebraic geometry, in particular in the study of algebraic vector bundles on complex projective spaces, which are strictly related (by means of presentations or resolutions by direct sums of line bundles) to matrices whose entries are homogeneous polynomials. The obvious strategy consists in translating the problems on vector bundles to problems on matrices (mostly related to computation of syzygies, which is the.core of the current Computer Algebra systems intended for algebraic geometry). Here we give some examples in the case of mathematical instanton bundles and their moduli spaces.