Related papers: Termination of 4-fold canonical flips

We compute global log canonical thresholds of some smooth Fano threefolds.

We improve on the result of Hacon and Witaszek by showing that the MMP for semi-stable fourfolds in mixed characteristic terminates in several new situations. In particular, we show the validity of the MMP for strictly semi-stable fourfolds…

We present an overview of the different renormalization proofs of the non commutative $\phi_4^{\star 4}$ model. This paper is a contribution to the MemPhys project.

We prove that every deformed mesh algebra of type $\mathbb{F}_4$ is isomorphic to the canonical mesh algebra of type $\mathbb{F}_4$.

In the manuscript [v4], we prove the uniqueness of a generalized quadrangle of order (4,16).

We prove that many simply connected symplectic four-manifolds dissolve after connected sum with only one copy of $S^{2}\times S^{2}$. For any finite group G that acts freely on the three-sphere we construct closed smooth four-manifolds with…

In this paper, we give an example of a chiral 4-polytope in projective 3-space. This example naturally yields a finite chiral 4-polytope in Euclidean 4-space, giving a counterexample to Theorem 11.2 of [2].

We give a method to resolve 4-dimensional symplectic orbifolds making use of techniques from complex geometry and gluing of symplectic forms. We provide some examples to which the resolution method applies.

We give a pen and paper and (comparatively) much simpler proof to verify of the Four Colour Theorem.

We prove a vanishing theorem for the twisted de Rham cohomology of a compact manifold.

We prove that all currently known examples of manifolds with nonnegative sectional curvature satisfy a stronger condition: their curvature operator can be modified with a 4-form to become positive-semidefinite.

We prove that the canonical 4-dimensional surgery problems can be solved after passing to a double cover. This contrasts the long-standing conjecture about the validity of the topological surgery theorem for arbitrary fundamental groups…

We shall investigate a flipping contraction g : X -> Y from a 4-fold X with at most isolated complete intersection singularities. If Y has an anti-bi-canonical divisor (=bi-elephant) with only rational singularities, then g carries an…

We show that if a compact, oriented 4-manifold admits a coassociative-free immersion into the Euclidean 7-space then its Euler characteristic and signature vanish. Moreover, in the spin case the Gauss map is contractible, so that the…

In this paper, we prove some foundational results on the deformation theory of E-infinity ring spectra.

We treat two different topics on the log minimal model program, especially for four-dimensional log canonical pairs. (a) Finite generation of the log canonical ring in dimension four. (b) Abundance theorem for irregular fourfolds. We obtain…

In this note, finite type epimorphisms of rings are characterized.

We study the lattices of algebraic and transcendental cycles of cubic fourfolds.

We prove divisorial canonicity of Fano hypersurfaces and double spaces of general position with elementary singularities.

We give some rationality constructions for Fano threefolds with canonical Gorenstein singularities.