Related papers: Twisted arithmetic Siegel Weil formula on X0(N)

We introduce new concepts in order to develop a general formalism for twisted differential operators in several variables. We investigate the notion of twisted coordinates on Huber rings that allows us to build various rings of twisted…

This paper is to study what we call twisted regular representations for vertex operator algebras. Let $V$ be a vertex operator algebra, let $\sigma_1,\sigma_2$ be commuting finite-order automorphisms of $V$ and let…

We compute the class of arithmetic genus two Teichmueller curves in the Picard group of pseudo-Hilbert modular surfaces, distinguished according to their torsion order and spin invariant. As an application, we compute the number of genus…

Let $\ell$ be an odd prime, $N \geq 1$ be an integer, and $\delta \geq 1$ be a $\ell^N$-th power free integer such that ${\rm ord}_{\ell}(\delta) = 0$ or $\ell \nmid {\rm ord}_{\ell}(\delta)$. In this paper, we give an explicit formula for…

Consider any representation $\phi$ of a finite-dimensional Lie algebra $g$ by derivations of the completed symmetric algebra $\hat{S}(g^*)$ of its dual. Consider the tensor product of $\hat{S}(g^*)$ and the exterior algebra $\Lambda(g)$. We…

In this paper, we investigate the theory of $g$-twisted modules for modular $\frac{1}{2}\mathbb{Z}$-graded vertex superalgebras over an algebraically closed field $\mathbb{F}$ of prime characteristic $p>2$. For a…

In this paper, we introduce novel concepts and establish a formal framework for twisted differential operators in the context of several variables. The focus is on twisted coordinates within Huber rings, which facilitate the construction of…

We provide a definition of Tanaka-Thomas's Vafa-Witten invariants for \'etale gerbes over smooth projective surfaces using the moduli spaces of $\mu_r$-gerbe twisted sheaves and Higgs sheaves. Twisted sheaves and their moduli are naturally…

We will introduce an operation "twisting" on Hochschild complex by analogy with Drinfeld's twisting operations. By using the twisting and derived bracket construction, we will study differential graded Lie algebra structures associated with…

We define a collection $\Theta_{g,n}\in H^{4g-4+2n}(\overline{\cal M}_{g,n},\mathbb{Q})$ for $2g-2+n>0$ of cohomology classes that restrict naturally to boundary divisors. We prove that the intersection numbers $\int_{\overline{\cal…

We present an explicit and computationally actionable blueprint for constructing vector-valued Siegel modular forms associated to real multiplication (RM) abelian surfaces, leveraging the theta correspondence for the unitary dual pair…

In this paper, we study the perturbative aspects of a twisted version of the two-dimensional $(0,2)$ heterotic sigma model on a holomorphic gauge bundle $\mathcal E$ over a complex, hermitian manifold $X$. We show that the model can be…

We construct the twisted Fock module of quantum toroidal $\mathfrak{gl}_1$ algebra with a slope $n'/n$ using vertex operators of quantum affine $\mathfrak{gl}_n$. The proof is based on the $q$-wedge construction of an integrable level-one…

We give a complete proof of the twisted duality property M(q)'= Z M(q^\perp) Z* of the (self-dual) CAR-Algebra in any Fock representation. The proof is based on the natural Halmos decomposition of the (reference) Hilbert space when two…

The tau function on the moduli space of generic holomorphic 1-differentials on complex algebraic curves is interpreted as a section of a line bundle on the projectivized Hodge bundle over the moduli space of stable curves. The asymptotics…

Fuchsian groups with a modular embedding have the richest arithmetic properties among non-arithmetic Fuchsian groups. But they are very rare, all known examples being related either to triangle groups or to Teichmueller curves. In Part I of…

Motivated by logarithmic conformal field theory and Gromov-Witten theory, we introduce a notion of a twisted module of a vertex algebra under an arbitrary (not necessarily semisimple) automorphism. Its main feature is that the twisted…

We propose a general procedure to construct noncommutative deformations of an algebraic submanifold $M$ of $\mathbb{R}^n$, specializing the procedure [G. Fiore, T. Weber, Twisted submanifolds of $\mathbb{R}^n$, arXiv:2003.03854] valid for…

We establish a bijection between torsion pairs in the category of finite-dimensional modules over a finite-dimensional algebra A and pairs (Z, I) formed by a closed rigid set Z in the Ziegler spectrum of A and a set I of indecomposable…

Using general principles in the theory of vertex operator algebras and their twisted modules, we obtain a bosonic, twisted construction of a certain central extension of a Lie algebra of differential operators on the circle, for an…