Seminarium Geometria Algebraiczna

In several areas of algebraic geometry (moduli theory, singularity theory), it is natural to work with pairs of a space X and a closed subspace $D \subset X$, and to think of $X \setminus D$ as the "main open of interest" and of $D$ as the "boundary". I will explain how the category of such pairs, which is badly behaved, can be better studied with the help of a more general notion of spaces with boundary called logarithmic schemes. We will see some natural examples from toric geometry and moduli theory.