Related papers: Modular interpretation of a non-reductive Chow quo…
We introduce cosurfaces with values in the group \(\PC_n(H)\) of \(H\)-valued reciprocal pairwise comparison matrices. The composition law is covariant on upper triangular coefficients and contravariant on lower triangular coefficients,…
We define degeneracy loci for vector bundles with structure group $G_2$, and give formulas for their cohomology (or Chow) classes in terms of the Chern classes of the bundles involved. When the base is a point, such formulas are part of the…
Given a certain kind of linear representation of a reductive group, referred to as a quasi-symmetric representation in recent work of \v{S}penko and Van den Bergh, we construct equivalences between the derived categories of coherent sheaves…
Recent work has shown that two-dimensional non-linear $\sigma$-models on group manifolds with Poisson-Lie symmetry can be understood within generalised geometry as exemplars of generalised parallelisable spaces. Here we extend this idea to…
We study curvature-adapted submanifolds of general symmetric spaces. We generalize Cartan's theorem for isoparametric hypersurfaces of spheres and Wang's classification of isoparametric Hopf hypersurfaces in complex projective spaces to any…
We study field theories defined in regions of the spatial non-commutative (NC) plane with a boundary present delimiting them, concentrating in particular on the U(1) NC Chern-Simons theory on the upper half plane. We find that classical…
A moduli space of stable quotients of the rank n trivial sheaf on stable curves is introduced. Over nonsingular curves, the moduli space is Grothendieck's Quot scheme. Over nodal curves, a relative construction is made to keep the torsion…
We prove that the open subvariety $\operatorname{Gr}_0(3,8)$ of the Grassmannian $\operatorname{Gr}(3,8)$ determined by the nonvanishing of all Pl\"ucker coordinates is sch\"on, i.e., all of its initial degenerations are smooth.…
This paper aims to develop a theory of projective and affine structures on higher-dimensional varieties in positive characteristic. This theory deals with Frobenius-projective and Frobenius-affine structures, which have been previously…
We prove a variant of a formula due to S. Zhang relating the Beilinson-Bloch height of the Gross-Schoen cycle on a pointed curve with the self-intersection of its relative dualizing sheaf. In our approach the height of the Gross-Schoen…
We analyse the diagonal quotient for products of certain Artin--Schreier curves. The smooth models are almost always surfaces of general type, with Chern slopes tending asymptotically to 1. The calculation of numerical invariants relies on…
We refine and generalize the results of e-Print: 2307.10428 [hep-th], where evidence in favor of applying the non-Abelian localization method to handle the 4d Chern-Simons theory path integral formulation was presented. We show, via duality…
We introduce a notion of `proChow group' of varieties, agreeing with the notion of Chow group for complete varieties and covariantly functorial with respect to arbitrary morphisms. We construct a natural transformation from the functor of…
We consider higher derivative CP(N) model in 2+1 dimensions with the Wess-Zumino-Witten term and the topological current density squared term. We quantize the theory by using the auxiliary gauge field formulation in the path integral method…
Let $A=(a_1,\ldots,a_n)$ be a vector of integers with $d=\sum_{i=1}^n a_i$. By partial resolution of the classical Abel-Jacobi map, we construct a universal twisted double ramification cycle $\mathsf{DR}^{\mathsf{op}}_{g,A}$ as an…
We study quotients of quasi-affine schemes by unipotent groups over fields of characteristic 0. To do this, we introduce a notion of stability which allows us to characterize exactly when a principal bundle quotient exists and, together…
The ring K(G/B) is isomorphic to a quotient of a Laurent polynomial ring by an ideal generated by certain W-symmetric functions and has a basis given by classes O_w, where O_w is the class of the structure sheaf of the Schubert variety X_w.…
We construct projective moduli spaces for torsion-free sheaves on noncommutative projective planes. These moduli spaces vary smoothly in the parameters describing the noncommutative plane and have good properties analogous to those of…
A question of Bergman asks whether the adjoint of the generic square matrix over a field can be factored nontrivially as a product of square matrices. We show that such factorizations indeed exist over any coefficient ring when the matrix…
The smooth action of a compact Lie group on a compact manifold can be resolved to an iterated space, as made explicit by Pierre Albin and the second author. On the resolution the lifted action has fixed isotropy type corresponding to the…