Related papers: Termination of 4-fold canonical flips
We prove that the class of log canonical rational singularities is closed under the basic operations of the minimal model program. We also give some supplementary results on the minimal model program for log canonical surfaces.
We describe a collection of constructions which illustrate a panoply of ``exotic'' smooth 4-manifolds.
We prove the long-standing Montesinos conjecture that any closed oriented PL 4-manifold M is a simple covering of S^4 branched over a locally flat surface (cf [J M Montesinos, 4-manifolds, 3-fold covering spaces and ribbons, Trans. Amer.…
We classify smooth Fano threefolds with infinite automorphism groups.
We prove that any finite, abstract n-polytope is covered by a finite, abstract regular n-polytope.
We prove a discrete approximation of functionals with jumps and creases.
We present a new topological proof of the infinitude of prime numbers with a new topology. Furthermore, in this topology, we characterize the infinitude of any non-empty subset of prime numbers.
We prove that a Kawamata log terminal pair has the canonical model.
We show that 3-fold terminal flips and divisorial contractions may be factored into a sequence of flops, blow-downs to a smooth curve in a smooth 3-fold or divisorial contractions to points with minimal discrepancies.
We prove that if a compact Riemannian 4-manifold with positive sectional curvature satisfies a Kato type inequality, then it is definite. We also discuss some new insights for compact Riemannian 4-manifolds of positive sectional curvature.
To construct a resulting model in LMMP is sufficient to prove existence of log flips and their termination for certain sequences. We prove that LMMP in dimension $d-1$ and termination of terminal log flips in dimension $d$ imply, for any…
We describe the final log canonical model of the moduli space of stable curves of genus four. We prove that the rational map from $\bar{M}_4$ to this model contracts the Petri and the boundary divisors and flips the hyperelliptic locus. As…
A proof via the Seiberg-Witten moduli space of Donaldson's theorem on smooth 4-manifolds with definite intersection forms.
We obtain upper bounds on the number of singular points of factorial terminal Fano threefolds.
Simultaneous diagonal flips in plane triangulations are investigated. It is proved that every $n$-vertex triangulation with at least six vertices has a simultaneous flip into a 4-connected triangulation, and that it can be computed in O(n)…
We prove the Complete nontrivial cycle-intersection theorem for systems of permutations.
In this article we classify quadruple Galois canonical covers $\phi$ of singular surfaces of minimal degree. This complements the work done in math.AG/0302045, so the main output of both papers is the complete classification of quadruple…
The paper has been withdrawn by the author due an error in the proof of Theorem 3.2.
We prove Simon's conjecture for 3-manifolds.
We give a classification, up to finite cover, of flat compact complete Hermite-Lorentz manifolds up to complex dimension 4.