Related papers: Nine-dimensional exceptional quotient singularitie…
We study exceptional quotient singularities. In particular, we prove an exceptionality criterion in terms of the $\alpha$-invariant of Tian, and utilize it to classify four-dimensional and five-dimensional exceptional quotient…
In this note, we prove that there exist infinite dimensional excellent rings.
We classify six-dimensional exceptional quotient singularities and show that seven-dimensional exceptional quotient singularities do not exist. Inter alia we prove that the irreducible six-dimensional projective representation of the…
We show that infinitely many Gorenstein weakly-exceptional quotient singularities exist in all dimensions, we prove a weak-exceptionality criterion for five-dimensional quotient singularities, and we find a sufficient condition for being…
The first examples of exceptional terminal singularities are constructed.
A singularity is said to be exceptional (in the sense of V. Shokurov), if for any log canonical boundary, there is at most one exceptional divisor of discrepancy -1. In our previous paper (math.AG/9805004) we found two examples of…
We prove that good quotients of algebraic varieties with 1-rational singularities also have 1-rational singularities. This refines a result of Boutot on rational singularities of good quotients.
We give an affirmative answer to Nash Problem for quotient surface singularities, in particular for the icosahedral singularity $E_8$.
We consider the uniqueness of solutions of ordinary differential equations where the coefficients may have singularities. We derive upper bounds on the the order of singularities of the coefficients and provide examples to illustrate the…
We determine the finite groups whose real irreducible representations have different degrees.
We prove the uniqueness of crepant resolutions for some quotient singularities and for some nilpotent orbits. The finiteness of non-isomorphic symplectic resolutions for 4-dimenensional symplectic singularities is proved. We also give an…
All varieties, extremal contractions, singularities are divided on exceptional and non-exceptional ones. Roughly speaking, there are the infinite families of non-exceptional varieties, extremal contractions or singularities and only the…
We provide a rough classification of threefold exceptionally non-canonical cDV quotient singularities by studying their combinatorial behavior.
We study the systems of ordinary differential equations which are implicit with respect to the higher derivatives, appearing in the linear form, and their solutions near the singular points. The invertibility of the higher derivatives…
We show that the existence of exceptional polynomials leads to the presence of non-trivial supersymmetry. The existence of these polynomials reveals several distinct isospectral potentials for the Schr\"odinger equation. All Schr\"odinger…
In this letter we prove existence and uniqueness of strong solutions to multi-dimensional SDEs with discontinuous drift and finite activity jumps.
Let Q be a connected directed quiver with n vertices. We show that Q is representation-infinite if and only if there do exist n isomorphism classes of exceptional modules of some fixed length at least 2.
We give a bound on the number of isolated, essential singularities of determinantal quartic surfaces in 3-space. We also provide examples of different configurations of real singularities on quartic surfaces with a definite Hermitian…
We show the existence of (non-Hermitian) strict quantization for every almost Poisson manifold.
We prove a "strong" Durfee-type inequality for isolated hypersurface surface singularities, which implies Durfee's strong conjecture for such singularities with non-negative topological Euler number of the exceptional set of the minimal…