Related papers: Supermoduli Space with Ramond punctures is not pro…
This expository note delves into the theory of projective modules parallel to the one developed for injective modules by Matlis. Given a perfect ring $R$, we present a characterization of indecomposable projective $R$-modules and describe a…
For the moduli space of unmarked convex $\mathbb{RP}^2$ structures on the surface $S_{g,m}$ with negative Euler characteristic, we investigate the subsets of the moduli space defined by the notions like boundedness of projective invariants,…
We define convex projective structures on 2D surfaces with holes and investigate their moduli space. We prove that this moduli space is canonically identified with the higher Teichmuller space for the group PSL_3 defined in our paper…
Moduli spaces of semistable sheaves on a K3 or abelian surface with respect to a general ample divisor are shown to be locally factorial, with the exception of symmetric products of a K3 or abelian surface and the class of moduli spaces…
We generalize the super period matrix of a super Riemann surface to the case that Ramond punctures are present. For a super Riemann surface of genus g with 2r Ramond punctures, we define, modulo certain choices that generalize those in the…
For the L_2-orthogonal projector P onto spaces of linear splines over simplicial partitions of polyhedral domains in R^d, d>1, we show that the L_infty norm of P cannot be bounded uniformly with respect to the partition. This is in contrast…
We compute the rational cohomology of the moduli space of non-singular complex projective curves of genus 3 with two marked points.
We introduce a similarity relation between submodules of a module $M$ over a ring $R$, extending the classical notion of similarity for right ideals. Focusing on (faithfully) projective modules, we establish a sharp lower bound for the…
Apart from global topological problems an affine homogeneous space is locally described by its curvature, its torsion and a slightly less tangible object called its connection in a given base point. Using this description of the local…
We show that there are many compact subsets of the moduli space $M_g$ of Riemann surfaces of genus $g$ that do not intersect any symmetry locus. This has interesting implications for $\mathcal{N}=2$ supersymmetric conformal field theories…
Let $M$ be a complete nonsingular fine moduli space of modules over an algebra $S$. A set of conditions is given for the Chow ring of $M$ to be generated by the Chern classes of certain universal bundles occurring in a projective resolution…
We classify orbifold geometries which can be interpreted as moduli spaces of four-dimensional $\mathcal{N}\geq 3$ superconformal field theories up to rank 2 (complex dimension 6). The large majority of the geometries we find correspond to…
A Margulis spacetime is a complete flat affine Lorentzian 3-manifold with free fundamental group. Associated to $M$ is a noncompact complete hyperbolic surface $\Sigma$. We study double extensions of $\pi_1 (M) \cong \pi_1 (\Sigma)$ when…
5D supergravity generically has non-geometric moduli other than the radion that belong to 5D vector multiplets. We summarize the impacts of such moduli on 4D effective theory of 5D supergravity on S^1/Z_2. We mainly discuss the structure of…
We study the properties of the Ramond fields in superstring theory in the presence of a constant B-field and the subsequent implications of space-time noncommutativity for space-time fermions and space-time supersymmetry. We find that the…
Assume $A$ is weakly symmetric, indecomposable, with radical cube zero and radical square non-zero. We show that such algebra of wild representation type does not have a non-projective module $M$ whose ext algebra is finite-dimensional.…
We determine the possible fractions of supersymmetry preserved by two intersecting M-5-branes. These include the fractions 3/32 and 5/32 which have not occurred previously in intersecting brane configurations. Both occur in non-orthogonal…
This work studies simply connected, noncompact $G/H$ in which $G$ is semi-simple, $H$ is connected, and $G/H$ has two irreducible summands. Here, we classify all such spaces and we provide solutions to the so-called Prescribed Ricci…
We express total set of rational Gromov-Witten invariants of projective spaces via periods of variations of semi-infinite Hodge structure associated with their mirror partners.
This paper examines various kinds of subspaces of the non-commutative spaces that are modelled on quasi-projective commutative schemes. It is shown how intersections and unions of weakly closed subspaces, closed subspaces, their weakly open…