Principal parts of a vector bundle on projective line and the fractional derivative

Abstract

This work is an exposition on computational aspects of principal parts of a vector bundle on projectiveline over the field of characteristic zero. Principal parts help determine the possibility of algebraically formalizinginfinitesimal-neighborhoods of subschemes inside some ambient scheme. The purpose of this study is to look for thepossibility of formalizing the algebraic geometric interpretation of fractional derivative. For the latter, this study followsthe approach proposed by Vasily Tarasov. The difference is that Tarasov proposed a geometric interpretation using finiteorderjet bundles from differential geometry. Present study proposes finite-order principal parts of the structure-sheaf ofreal projective line as its formal algebraic geometric parallel.