Related papers: Witt groups of complex cellular varieties

A quadratic form over a Henselian-valued field of arbitrary residue characteristic is tame if it becomes hyperbolic over a tamely ramified extension. The Witt group of tame quadratic forms is shown to be canonically isomorphic to the Witt…

In this paper, we establish a complete structural description of flat Lorentzian Lie groups, i.e., Lie groups endowed with a flat left invariant Lorentzian metric, thereby resolving a long-standing open problem in the theory of…

We describe an algorithm which pattern embeds, in the sense of Woo-Yong, any Bruhat interval of a symmetric group into an interval whose extremes lie in the same right Kazhdan-Lusztig cell. This apparently harmless fact has applications in…

The compactly supported $\mathbb{A}^1$-Euler characteristic, introduced by Hoyois and later refined by Levine and others, is an anologue in motivic homotopy theory of the classical Euler characteristic of complex topological manifolds. It…

In this note the smooth (i.e. with open stabilizers) linear and {\sl semilinear} representations of certain permutation groups (such as infinite symmetric group or automorphism group of an infinite-dimensional vector space over a finite…

We show that the fundamental group of any smooth subelliptic variety is finite. Moreover, it is also proved that every finite group can be realized as the fundamental group of a smooth subelliptic variety. As a consequence, it follows that…

Let $\text{GL}(n) = \text{GL}(n, {\mathbb C})$ denote the complex general linear group and let $G \subset \text{GL}(n)$ be one of the classical complex subgroups $\text{O}(n)$, $\text{SO}(n)$, and $\text{Sp}(2k)$ (in the case $n = 2k$). We…

Extending results of Wyser, we determine formulas for the equivariant cohomology classes of closed orbits of certain families of spherical subgroups of $GL_n$ on the flag variety $GL_n/B$. Putting this together with a slight extension of…

We record an observation about the Witten indices in two families of gauged linear sigma models: the U(2) model for linear sections of Grassmannians, and the U(1) model for quadric complete intersections. We describe how the Witten indices…

We give an example of proper smooth fourfold over a perfect field k of characteristic p > 0 with asymmetric Hodge--Witt numbers in total degree 3. Our example is sharp both in terms of dimension and total degree. We arrive at our example by…

In this short work we prove that the Hilbert Grassmannians endowed with the weak topology are models for the classifying spaces of the unitary groups. As application of this result one can use Hilbert Grassmannians for the presentation of…

This paper develops a discrete theory of real Riemann surfaces based on quadrilateral cellular decompositions (quad-graphs) and a linear discretization of the Cauchy-Riemann equations. We construct a discrete analogue of an antiholomorphic…

We prove that compact quaternionic-K\"ahler manifolds of positive scalar curvature admit no almost complex structure, even in the weak sense, except for the complex Grassmannians $Gr_2(C^{n+2})$. We also prove that irreducible inner…

We study the Grothendieck group of the variety $X_{n,k}$ of spanning line configurations introduced by Pawlowski--Rhoades [arXiv:1711.08301] as a geometric model for the generalized coinvariant algebra $R_{n,k}$. Our first result is a…

Relations among tautological classes on the moduli space of stable curves are obtained via the study of Witten's r-spin theory for higher r. In order to calculate the quantum product, a new formula relating the r-spin correlators in genus 0…

The Grassmannian model represents harmonic maps from Riemann surfaces by families of shift-invariant subspaces of a Hilbert space. We impose a natural symmetry condition on the shift-invariant subspaces that corresponds to considering an…

In this article we study the vertices of simple modules for the symmetric groups in prime characteristic $p$. In particular, we complete the classification of the vertices of simple $S_n$-modules labelled by hook partitions.

We give a bijection between certain colored partitions and the elements in the quotient of an affine Weyl group modulo its Weyl group. By Bott's formula these colored partitions give rise to some partition identities. In certain types,…

We realize a graded variant $K_0(Var_k^{dim})$ of the Grothendieck ring of varieties as a quadratic extension of the subring $K_0(Var_k^{sp})$ spanned by classes of smooth and proper varieties. As such, there exists a natural involution…

We show that the algebraic and the symplectic GW-inivariants of smooth projective varieties are equivalent.