We will introduce basic notions of algebraic geometry starting with Hilbert’s Nullstellensatz, affine and projective varieties. We can think of an affine variety as the common zeros of a set of given polynomials in multiple variables. We will further introduce rational maps between varieties leading to the important topic of birational geometry. Finally, we will learn what a singular point of an affine variety is. Along the way, we will look at many simple and concrete examples.
Objective/Learning outcomes:
Gaining familiarity with the language and concepts and of algebraic geometry building on commutative algebra. Applying the general theory to concrete simple examples.
Public cible/Target audience:
Master students in mathematics