Related papers: Orbit closures and rational surfaces

The Grassmann manifold of linear subspaces is important for the mathematical modelling of a multitude of applications, ranging from problems in machine learning, computer vision and image processing to low-rank matrix optimization problems,…

We prove that the orbit closure of the determinant is not normal. A similar result is obtained for the orbit closure of the permanent multiplied by a power of a linear form.

We study moduli spaces of lattice-polarized K3 surfaces in terms of orbits of representations of algebraic groups. In particular, over an algebraically closed field of characteristic 0, we show that in many cases, the nondegenerate orbits…

In a previous paper, we showed how certain orientations of the edges of a graph G embedded in a closed oriented surface S can be understood as discrete spin structures on S. We then used this correspondence to give a geometric proof of the…

The main objective of this project is to determine all irreducible modules of a given modular Lie algebra. In contrast to ordinary Lie algebras, modular Lie algebras require an additional structure known as the p-mapping. The minimal…

We study finite-dimensional representations of hyper loop algebras over non-algebraically closed fields. The main results concern the classification of the irreducible representations, the construction of the Weyl modules, base change,…

We study two families of $g$-dimensional abelian varieties, induced by distinct rational maps defined on a common variety $\overline{\mathcal A}$ and mapping to two bases $\overline{S}_1$ and $\overline{S}_2$. Two non-torsion sections…

This is an introduction to the geometry of compact Riemann surfaces, largely following the books Farkas-Kra, Fay, Mumford Tata lectures. 1) Defining Riemann surfaces with atlases of charts, and as locus of solutions of algebraic equations.…

Let I be a finite set and CI be the algebra of functions on I. For a finite dimensional C algebra A with \CI contained in A we show that certain moduli spaces of finite dimsional modules are isomorphic to certain Grassmannian (quot-type)…

We give an elementary explicit construction of cell decomposition of the moduli space of projective structures on a two dimensional surface analogous to the decomposition of Penner/Strebel for moduli space of complex structures. The…

We give necessary conditions on complete embedded \cmc surfaces with three or four ends subject to reflection symmetries. The respective submoduli spaces are two-dimensional varieties in the moduli spaces of general \cmc surfaces. We…

The rational homology of unordered configuration spaces of points on any surface was studied by Drummond-Cole and Knudsen. We compute the rational cohomology of configuration spaces on a closed orientable surface, keeping track of the mixed…

For a finitely-generated vertex operator algebra of central charge c, a locally convex topological completion is constructed. We construct on the completion a structure of an algebra over the operad of the c/2-th power of the determinant…

In [BFMT17] we introduced orbital degeneracy loci as generalizations of degeneracy loci of morphisms between vector bundles. Orbital degeneracy loci can be constructed from any stable subvariety of a representation of an algebraic group. In…

Let $ \tilde{G} $ be an algebraic group acting on a variety $ \tilde{L} $, and $ G \subset \tilde{G} $ a subgroup which leaves a subvariety $ L \subset \tilde{L} $ stable. For a $ G $-orbit $ O_G = G u (u \in L) $ in $ L $, we can associate…

We introduce the notion of cyclic cohomology of an A-infinity algebra and show that the deformations of an A-infinity algebra which preserve an invariant inner product are classified by this cohomology. We use this result to construct some…

Let $R$ be a polynomial ring over a field. We describe the extremal rays and the facets of the cone of local cohomology tables of finitely generated graded $R$-modules of dimension at most two. Moreover, we show that any point inside the…

In this article, we establish a connection between two models for $r$-spin structures on surfaces: the marked PLCW decompositions of Novak and Runkel-Szegedy, and the structured graphs of Dyckerhoff-Kapranov. We use these models to describe…

Let K be a number field, let f: P_1 --> P_1 be a nonconstant rational map of degree greater than 1, let S be a finite set of places of K, and suppose that u, w in P_1(K) are not preperiodic under f. We prove that the set of (m,n) in N^2…

We reconsider non-degenerate second order superintegrable systems in dimension two as geometric structures on conformal surfaces. This extends a formalism developed by the authors, initially introduced for (pseudo-)Riemannian manifolds of…