Related papers: Remarks on mod-2 elliptic genus

We introduce the quasi-Hopf superalgebras which are $Z_2$ graded versions of Drinfeld's quasi-Hopf algebras. We describe the realization of elliptic quantum supergroups as quasi-triangular quasi-Hopf superalgebras obtained from twisting the…

We study the minimal Weierstrass equations for genus 2 curves defined over a ring of integers $\mathcal O_{\mathbb F}$. This is done via reduction theory and Julia invariant of binary sextics. We show that when the binary sextics has extra…

Building on the work of Mann and Rafi, we introduce an expanded definition of a telescoping 2-manifold and proceed to study the homeomorphism group of a telescoping 2-manifold. Our main result shows that it is strongly distorted. We then…

Seiberg-Witten geometry of mass deformed $\mathcal N=2$ superconformal ADE quiver gauge theories in four dimensions is determined. We solve the limit shape equations derived from the gauge theory and identify the space $\mathfrak M$ of…

Using spectral invariants of Dirac operators we construct a secondary version of the Witten genus, a bordism invariant of string manifolds in dimensions $4m-1$. We prove a secondary index theorem which relates this global-analytic…

We compute the transgressed forms of some modularly invariant characteristic forms,which are related to the twisted elliptic genera. We study the modularity properties of these secondary characteristic forms and relations among them. We…

We construct a modified double elliptic gamma function which is well defined when one of the base parameters lies on the unit circle. A model consisting of 6d hypermultiplets coupled to a gauge field theory living on a 4d defect is proposed…

We study stable curves of arithmetic genus 2 which admit two morphisms of finite degree $p$, resp. $d$, onto smooth elliptic curves, with particular attention to the case $p$ prime.

We calculate the elliptic genus of two dimensional abelian gauged linear sigma models with (2,2) supersymmetry using supersymmetric localization. The matter sector contains charged chiral multiplets as well as Stueckelberg fields coupled to…

Higher-derivative generalization of the supersymmetric quantum mechanics is proposed. It is formally based on the standard superalgebra but supercharges involve differential operators of the order $n$. As a result, their anticommutator…

We outline a general algorithm for computing an explicit model over a number field of any curve of genus 2 whose (unpolarized) Jacobian is isomorphic to the product of two elliptic curves with CM by the same order in an imaginary quadratic…

The Gauge/Bethe correspondence relates Omega-deformed N=2 supersymmetric gauge theories to some quantum integrable models, in simple cases the integrable models can be treated as solvable quantum mechanics models. For SU(2) gauge theory…

We study an integer sequence associated with Cantor's division polynomials of a genus 2 curve having an integral point. We show that the reduction modulo $p$ of such a sequence is periodic for all but finitely many primes $p$, and describe…

Explicit models of families of genus 2 curves with multiplication by $\sqrt D$ are known for $D= 2, 3, 5$. We obtain generic models for genus 2 curves over $\mathbb Q$ with real multiplication in 12 new cases, including all fundamental…

We construct "connected" (0,2) sigma models starting from n copies of (2,2) CP(N-1) models. General aspects of models of this type (known as T+O deformations) had been previously studied in the context of heterotic string theories. Our…

We study the codimension n locus of curves of genus 2 with n distinct marked Weierstrass points inside the moduli space of genus 2, n-pointed curves, for n <= 6. We give a recursive description of the classes of the closure of these loci…

By considering a (partial) topological twisting of supersymmetric Yang-Mills compactified on a 2d space with `t Hooft magnetic flux turned on we obtain a supersymmetric $\sigma$-model in 2 dimensions. For N=2 SYM this maps Donaldson…

We consider the genus of $20$ classes of unimodular Hermitian lattices of rank $12$ over the Eisenstein integers. This set is the domain for a certain space of algebraic modular forms. We find a basis of Hecke eigenforms, and guess global…

Families of hyper-elliptic curves which describe the quantum moduli spaces of vacua of $N=2$ supersymmetric $SO(N_c)$ gauge theories coupled to $N_f$ flavors of quarks in the vector representation are constructed. The quantum moduli spaces…

In Physics and in Mathematics $\mathbb{Z}_2^n$-gradings, $n>1$, appear in various fields. The corresponding sign rule is determined by the `scalar product' of the involved $\mathbb{Z}_2^n$-degrees. The $\mathbb{Z}_2^n$-Supergeometry…