geometry, the problem of resolution of singularities asks whether every algebraic variety V has a resolution, which is a non-singular variety W with a proper...

its cones of maximal dimension are generated by a basis of the lattice. This implies that every toric variety has a resolution of singularities given by...

acquire singular points on the hyperplane at infinity, when its closure in projective space is taken. Resolution says that such singularities can be handled...

One of the canonical examples of a birational map is the Resolution of singularities. Over a field of characteristic 0, every singular variety X...

problem of resolution of singularities can be solved; Hironaka (1964) showed this in characteristic 0, but the positive characteristic case is (as of 2024)...

Standard resolution, the bar construction of resolutions in homological algebra Resolution of singularities in algebraic geometry Resolution (audio),...

discussed cutting-edge research developments including the resolution of singularities problem for which Hironaka later received the Fields Medal. Hironaka...

convenient setting. Much deeper is Hironaka's 1964 theorem on resolution of singularities: over a field of characteristic 0 (such as the complex numbers), every...

Dan (2017). "Resolution of singularities of complex algebraic varieties and their families". Proceedings of the International Congress of Mathematicians...

important way of constructing new spaces. For instance, most procedures for resolution of singularities proceed by blowing up singularities until they become...