Graduate Algebra Symposium

Richard Chandler

Determining the Multiplicity of Points in Projective Schemes

In algebraic geometry, an algebraic scheme encodes a great deal more information than an algebraic variety. In particular, an algebraic scheme encodes the multiplicity of the points contained within it while the algebraic variety does not; these multiplicities can in turn give us information about the algebra we have associated the scheme to. However, analyzing a scheme in general can be cumbersome, as can finding the multiplicity of specific points. In this talk we will discuss how coupling the process of localization with Bezout's Theorem gives us a method for determining this multiplicity.