Related papers: Non-orientable Nurikabe
We study cyclic covering morphisms from $\bar{M}_{0,n}$ to moduli spaces of unpointed stable curves of positive genus or compactified moduli spaces of principally polarized abelian varieties. Our main application is a construction of new…
A construction of compact tachyon-free orientifolds of the non-supersymmetric Type 0B string theory is presented. Moreover, we study effective non-supersymmetric gauge theories arising on self-dual D3-branes in Type 0B orbifolds and…
Trace formulas are investigated in non-commutative integration theory. The main result is to evaluate the standard trace of a Takesaki dual and, for this, we introduce the notion of interpolator and accompanied boundary objects. The formula…
The nonabelian Jacobian $\JA$ of a smooth projective surface $X$ is inspired by the classical theory of Jacobian of curves. It is built as a natural scheme interpolating between the Hilbert scheme $\XD$ of subschemes of length $d$ of $X$…
We present the M\"{o}bius functions of several posets of annular noncrossing objects, namely a self-dual extension of the annular noncrossing permutations, minimal length annular partitioned permutations, and annular noncrossing partitons.
The Narasimhan-Nori conjecture asks for a closed formula for the number of non-isomorphic principal polarizations of any given abelian variety. In this paper, we introduce a new algorithm that gives a lower bound on the number of…
We implement a noncommutative analogue of the well-known commutative cyclic covering trick and implement it to explicitly construct a vast collection of numerically Calabi-Yau orders, noncommutative analogues of surfaces of Kodaira…
Various structural properties are developed for non-orientable surfaces in link spaces. The M\"obius band tree is described to represent genus growth of one-sided surfaces in solid tori. The structure of the Tree allows various insights…
We consider noncommutative theory of a compact scalar field. The recently discovered projector solitons are interpreted as classical vacua in the model considered. Localized solutions to the projector equation are pointed out and their…
The split version of the Freudenthal-Tits magic square stems from Lie theory and constructs a Lie algebra starting from two split composition algebras [3, 17, 18]. The geometries appearing in the second row are Severi-Brauer varieties [20].…
We study an extended Heisenberg model on the MnSi lattice. In the cubic B20 crystal structure of MnSi, Mn atoms form lattices of of corner-shared equilateral triangles. We find an ubiquitous spiral ordering along (110) for J1 <0, and J2=J3…
The mirror curves enable us to study B-model topological strings on non-compact toric Calabi--Yau threefolds. One of the method to obtain the mirror curves is to calculate the partition function of the topological string with single brane.…
In this paper, we present a method to identify integrable complex nonlinear oscillator systems and construct their solutions. For this purpose, we introduce two types of nonlocal transformations which relate specific classes of nonlinear…
We consider D-branes and orientifold planes embedded in non-compact (orbifolded) space-time. We point out that even in the non-compact cases we can turn on non-zero (quantized) NS-NS antisymmetric B-field. In particular, we study the effect…
We present new solutions of noncommutative gauge theories in which coincident unstable vortices expand into unstable circular shells. As the theories are noncommutative, the naive definition of the locations of the vortices and shells is…
In this paper, we will describe a combinatorial object to list the orbits in the ${\mathbb Z}$-graded Lie algebra, their Jordan bloc decomposition, their dimension, their dimension, the partial order and the equivariant local system (up to…
Let $\bar{P}$ be a sequence of length $2n$ in which each element of $\{1,2,...,n\}$ occurs twice. Let $P'$ be a closed curve in a closed surface $S$ having $n$ points of simple auto-intersections, inducing a 4-regular graph embedded in $S$…
We investigate generalizations of the Charlier and the Meixner polynomials on the lattice N and on the shifted lattice N+1-\beta. We combine both lattices to obtain the bi-lattice N \cup (N+1-\beta) and show that the orthogonal polynomials…
We survey noncommutative spacetimes with coordinates being enveloping algebras of Lie algebras. We also explain how to do differential geometry on noncommutative spaces that are obtained from commutative ones via a Moyal-product type…
We continue explorations of deformed Abrikosov-Nielsen-Olesen (ANO) strings, with non-Abelian moduli on the world sheet. In a simple model with an extra field we find classically stable ANO and non-Abelian strings. The tension of the latter…