A systematic procedure in birational geometry aimed at simplifying the structure of algebraic varieties by successive contractions and flips, ultimately leading to a model with mild singularities.

These singularities offer a refined lens through which to view the geometry of algebraic varieties, helping to classify and understand their complex global structures. In recent years, significant ...

Resolution of singularities is notorious as a difficult topic within algebraic geometry. Recent work, aiming at resolution of families and semistable reduction, infused the subject with logarithmic ...

My research has been mainly in algebraic geometry, with an abiding interest in the study of algebraic cycles, particularly in the presence of singularities. I have established a number of results in ...

Variants of this appear in several mathematical disciplines. In algebraic geometry, $\mathfrak{M}_g$ is constructed using geometric invariant theory and has a well-studied compactification introduced ...

In their paper, Mizera and his colleagues used mathematical tools including topology, geometry, and algebra to better understand a particular kind of singularity, namely Landau singularities.

One of the bigger questions within algebraic geometry is how to “resolve” singularities — that is, how to get rid of them. Mathematically, resolving a singularity means smoothing over the ...