Related papers: Shokurov's index conjecture for quotient singulari…
We will give a pure combinatorial proof of the Eisenbud-Goto conjecture for arbitrary monomial curves. Moreover, we will show that the conjecture holds for certain simplicial affine semigroup rings.
We prove the ACC conjecture for local volumes. Moreover, when the local volume is bounded away from zero, we prove Shokurov's ACC conjecture for minimal log discrepancies.
We prove the Burghelea Conjecture for groups satisfying some additional cohomological property.
We give some necessary conditions for the existence of a symplectic resolution for quotient singularities. The McKay correspondence is also worked out for these resolutions.
We prove a part of Shokurov's conjecture on characterization of toric varieties modulo the minimal model program and adjunction conjecture.
We show how tools from computational group theory can be used to prove that a subgroup of matrices has infinite index.
We prove an analog of Gromov--Lawson type relative index theorems for K-homology classes.
We prove Union-Closed sets conjecture.
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 the Aharoni Berger Conjecture
We propose new conjectures about the relationship between the principal blocks of finite groups for different primes and establish evidence for these conjectures.
This note presents an elementary and direct proof for the convexity of the Choquet integral when the corresponding set function is submodular.
We prove the existence of tilting objects on some global quotient stacks. As a consequence we provide further evidence for a conjecture on the Rouquier dimension of derived categories formulated by Orlov.
We prove Marchenko-type uniqueness theorems for inverse Sturm-Liouville problems. Moreover, we prove a generalization of Ambarzumyans theorem.
We establish an analogue of the Goldbach conjecture for Laurent polynomials with positive integer coefficients.
We give counterexamples to Okounkov's log-concavity conjecture for Littlewood-Richardson coefficients.
We prove the topological analogue of the period-index conjecture in each dimension away from a small set of primes.
We discuss the validity of the proof of the fixed numerator conjecture on Markov numbers, which is the main result of the paper mentioned in the title.
We consider generalizations of Szpiro's classical discriminant conjecture to hyperelliptic curves over a number field $K$, and to smooth, projective and geometrically connected curves $X$ over $K$ of genus at least one. The main results…
We prove Cherlin's conjecture, concerning binary primitive permutation groups, for those groups with socle isomorphic to a sporadic simple group.