The character and the wave front set correspondence in the stable range

We relate the distribution characters and the wave front sets of unitary representation for real reductive dual pairs of type I in the stable range.     

Automorphisms of Hilbert schemes of points on a generic projective K3 surface

We study automorphisms of the Hilbert scheme of n points on a generic projective K3 surface S, for any . We show that is either trivial or generated by a non‐symplectic involution and we determine numerical and divisorial conditions which allow us to distinguish between the two cases. As an application of these results we prove that, for any , there exist infinitely many admissible degrees for the polarization of the K3 surface S such that 22732715-aa51-426e-828e-e6b98070bb4d/mana201800557-math-0004.png"> admits a non‐natural involution. This provides a generalization of the results of [7] for .     

Indecomposable involutive set-theoretic solutions of the Yang–Baxter equation

We describe the indecomposable involutive non-degenerate set-theoretic solutions of the Yang–Baxter equation as dynamical extensions of non-degenerate left cycle sets. Moreover we characterize the indecomposable dynamical extensions and we produce several examples. As an application we construct a family of finite indecomposable solutions whose structure groups have not the unique product property.     

Carlsson's rank conjecture and a conjecture on square-zero upper triangular matrices

Let k be an algebraically closed field and A the polynomial algebra in r variables with coefficients in k. In case the characteristic of k is 2, Carlsson [9] conjectured that for any DG-A-module M of dimension N as a free A-module, if the homology of M is nontrivial and finite dimensional as a k-vector space, then $2^r\le N$. Here we state a stronger conjecture about varieties of square-zero upper triangular $N\times N$ matrices with entries in A. Using stratifications of these varieties via Borel orbits, we show that the stronger conjecture holds when $N<8$ or $r<3$ without any restriction on the characteristic of k. As a consequence, we obtain a new proof for many of the known cases of Carlsson's conjecture and give new results when $N>4$ and $r=2$.     

Modules over quantaloids: Applications to the isomorphism problem in algebraic logic and π-institutions

We solve the isomorphism problem in the context of abstract algebraic logic and of π-institutions, namely the problem of when the notions of syntactic and semantic equivalence among logics coincide. The problem is solved in the general setting of categories of modules over quantaloids. We introduce closure operators on modules over quantaloids and their associated morphisms. We show that, up to isomorphism, epis are morphisms associated with closure operators. The notions of (semi-)interpretability and (semi-)representability are introduced and studied. We introduce cyclic modules, and provide a characterization for cyclic projective modules as those having a g-variable. Finally, we explain how every π-institution induces a module over a quantaloid, and thus the theory of modules over quantaloids can be considered as an abstraction of the theory of π-institutions.     

On Cartan's theorem for linear operators

In this paper, we describe a second main theorem of holomorphic curves in , of hyper‐order strictly less than 1, that involves a general linear operator . As an application, we derive a truncated second main theorem of degenerate holomorphic curves of hyper‐order strictly less than 1 using Nochka weights.     

Strict topologies on measure spaces

Let X be a measurable space, let 227:mana201600227-math-0001" class="section_image" src="/cms/asset/3a996abf-cbeb-4ab5-9a4b-59bda1f1c649/mana201600227-math-0001.png"> be a family of measurable subsets of it, and let 227:mana201600227-math-0002" class="section_image" src="/cms/asset/970be77c-80cf-4c42-86e3-49473a329277/mana201600227-math-0002.png"> be a subspace of complex measures on X that is also closed under restrictions of measures. In this paper we introduce the 227:mana201600227-math-0003" class="section_image" src="/cms/asset/fa9a9cf4-0546-4a69-9b46-623589583404/mana201600227-math-0003.png">‐convergence topology 227:mana201600227-math-0004" class="section_image" src="/cms/asset/992eee29-f447-403e-8088-93fe3e8b1483/mana201600227-math-0004.png"> and the 227:mana201600227-math-0005" class="section_image" src="/cms/asset/9e35217d-df15-4bc7-9183-f1af68a18d98/mana201600227-math-0005.png">‐strict topology 227:mana201600227-math-0006" class="section_image" src="/cms/asset/3154267c-04ba-4de0-86e5-0a700c789d75/mana201600227-math-0006.png"> on 227:mana201600227-math-0007" class="section_image" src="/cms/asset/fc601ef5-c7e5-4809-908a-04047915c119/mana201600227-math-0007.png">. Among other results, we find necessary and sufficient conditions for Hausdorff‐ness and coincide‐ness of these topologies. Applications to Lebesgue spaces, and also examples in Hausdorff topological spaces and locally compact groups are given.