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...

representation theory, a symplectic resolution is a morphism that combines symplectic geometry and resolution of singularities. Let π : Y → X {\displaystyle...

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

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

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

variety has a resolution of singularities given by another toric variety, which can be constructed by subdividing the maximal cones of its associated...

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...

Bott–Samelson resolution of a Schubert variety is a resolution of singularities. It was introduced by Bott & Samelson (1958) in the context of compact Lie...

of resolution of singularities, stating that a variety can be desingularized near any valuation, or in other words that the Zariski–Riemann space of the...

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

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

Oscar (1972), Collected papers. Vol. I: Foundations of algebraic geometry and resolution of singularities, Cambridge, Massachusetts-London: MIT Press,...

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

of a variety is nonsingular in some sense, so is a sort of rather weak resolution of singularities. This does not solve the problem of resolution of singularities...

singularities. Normalization is not usually used for resolution of singularities for schemes of higher dimension. To define the normalization, first suppose...

surfaces, rational singularities were defined by (Artin 1966). Alternately, one can say that X {\displaystyle X} has rational singularities if and only if...

rational singularities A variety X over a field of characteristic zero has rational singularities if there is a resolution of singularities f : X ′ →...

Abramovich, Dan. "Review: Resolution of singularities by Steven Dale Cutkovsky and Lectures on resolution of singularities by János Kollár" (PDF). Bull...

has canonical singularities (for example, rational Gorenstein singularities), there is a variety Y with Q-factorial terminal singularities and a birational...

mathematics, canonical singularities appear as singularities of the canonical model of a projective variety, and terminal singularities are special cases that...

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

studied singularities on algebraic curves and surfaces. In particular, he supplied a proof (questioned by some) that a procedure for resolution of singularities...

Lojasiewicz, Triangulation of semi-analytic sets, Ann. Scu. Norm. di Pisa, 18 (1964), 449–474. Heisuke Hironaka, Resolution of singularities of an algebraic variety...

the tangent cone is not singular outside its vertex. Milnor map Resolution of singularities Singular point of a curve Singularity theory Smooth scheme Zariski...

considerably down to about 10 or 20 pages. 1966 Abyhankar's proof of resolution of singularities for 3-folds in characteristic greater than 6 covered about 500...

a Dynkin diagram of A-D-E singularity type. They are the canonical singularities (or, equivalently, rational Gorenstein singularities) in dimension 2....

with birational geometry, the resolution of singularities, subvarieties of abelian varieties, limits for the torsion of elliptic curves, rational and...

from the original on 22 March 2019. Retrieved 7 April 2019. "Memorial Resolution – Paul Cohen (1934–2007)" (PDF). Stanford Historical Society. 2011. Archived...

field of an algebraic variety Ample line bundle Ample vector bundle Linear system of divisors Birational geometry Blowing up Resolution of singularities Rational...

care of noncompactness and singularities. Both parts use the resolution of singularities (due to Hironaka) in an essential way. In the singular case,...