Related papers: Prime order birational diffeomorphisms of the sphe…

A criterion for M\"uger centralizer of a fusion subcategory of a braided non-degenerate fusion category is given. Along the way we extend some identities on the space of class functions of a fusion category introduced by Shimizu in…

Duistermaat introduced the concept of ``real locus'' of a Hamiltonian manifold. In that and in others' subsequent works, it has been shown that many of the techniques developed in the symplectic category can be used to study real loci, so…

We construct two kinds of group cocycles on the volume-preserving diffeomorphism group. We show that, for the volume-preserving diffeomorphism group of the sphere, one of the cocycles gives the Euler class of flat sphere bundles.

It is well known that numerical quantities arising from the theory of D-modules are related to invariants of singularities in birational geometry. This paper surveys a deeper relationship between the two areas, where the numerical…

In this paper, we study the structure of homogeneous subgroups of the homeomorphism group of the sphere, which are defined as closed groups of homeomorphisms of the sphere that contain the rotation group. We prove two structure theorems…

We classify nonsymplectic automorphisms of prime order on irreducible holomorphic symplectic manifolds of O'Grady's 6-dimensional defamation type. More precisely, we give a classification of the invariant and coinvariant sublattices of the…

When studying families in the moduli space of dynamical systems, choosing an appropriate representative function for a conjugacy class can be a delicate task. The most delicate questions surround rationality of the conjugacy class compared…

We introduce the concept of a standard form for two embedded maximal sphere systems in the doubled handlebody, and we prove an existence and uniqueness result. In particular, we show that pairs of maximal sphere systems in the doubled…

Let \alpha be a Schur root; let h=hcf_v(\alpha(v)) and let p = 1 - < \alpha/h,\alpha/h >. Then a moduli space of representations of dimension vector \alpha is birational to p h by h matrices up to simultaneous conjugacy. Therefore, if…

We classify the total spaces of bundles over the four sphere with fiber a three sphere up to orientation preserving and reversing homotopy equivalence, homeomorphism and diffeomorphism. These total spaces have been of interest to both…

An introduction to moduli spaces of representations of quivers is given, and results on their global geometric properties are surveyed. In particular, the geometric approach to the problem of classification of quiver representations is…

In this paper we construct the category of birational spaces as the category in which Temkin's relative Riemann-Zariski spaces are naturally included. Furthermore we develop an analogue of Raynaud's theory. We prove that the category of…

We construct a diagrammatic categorification of the spherical module over the Hecke algebra. We establish a basis for the morphism spaces of this category, and prove that it is equivalent to an existing algebraic spherical category.

In the present paper we propose a combinatorial approach to study the so called double octic Clabi--Yau threefolds. We use this description to give a complete classification of double octics with $h^{1,2}\le1$ and to derive their geometric…

We give a lattice-theoretic characterization for a manifold of $\mathrm{OG}10$ type to be birational to some moduli space of (twisted) sheaves on a K3 surface. We apply it to the Li-Pertusi-Zhao variety of $\mathrm{OG}10$ type associated to…

The structure of topological spaces is analysed here through the lenses of fibrous preorders. Each topological space has an associated fibrous preorder and those fibrous preorders which return a topological space are called spacial. A…

In this note, we study the general form of a multiplicative bijection on several families of functions defined on manifolds, both real or complex valued. In the real case, we prove that it is essentially defined by a composition with a…

We give a sharp bound for orders of elementary abelian 2-groups of birational automorphisms of rationally connected threefolds.

We give a complete classification of conformally covariant differential operators between the spaces of $i$-forms on the sphere $S^n$ and $j$-forms on the totally geodesic hypersphere $S^{n-1}$. Moreover, we find explicit formul{\ae} for…

We explore some concepts of module theory that derive from the notion of primeness, such as first modules, and extend them to more general environments. We also provide descriptions of simple left semiartinian rings, left local rings,…