Related papers: Ice cream and orbifold Riemann-Roch

The deformation approach of arXiv:2104.07816 for computing zeta functions of one-parameter Calabi-Yau threefolds is generalised to cover also multiparameter manifolds. Consideration of the multiparameter case requires the development of an…

We are considering the class of heterotic $\mathcal{N}=(2,2)$ Landau-Ginzburg orbifolds with 9 fields corresponding to $A_1^9$ Gepner models. We classify all of its Abelian discrete quotients and obtain 152 inequivalent models closed under…

For any finite abelian group G, the equivariant Gromov-Witten invariants of C^r/G can be viewed as a certain kind of abelian Hurwitz-Hodge integrals. In this note, we use Tseng's orbifold quantum Riemann-Roch theorem to express this kind of…

We describe the graded characters and Hilbert functions of certain graded artinian Gorenstein quotients of the polynomial ring which are also representations of the symmetric group. Specifically, we look at those algebras whose socles are…

We combine our results on symmetric products and second quantization with our description of discrete torsion in order to explain the ring structure of the cohomology of the Hilbert scheme of points on a K3 surface. This is achieved in…

We prove a conjecture of Hutchings and Lee relating the Seiberg-Witten invariants of a closed 3-manifold X with b_1 > 0 to an invariant that `counts' gradient flow lines--including closed orbits--of a circle-valued Morse function on the…

Graded skew-commutative rings occur often in practice. Here are two examples: 1) The cohomology ring of a compact three-dimensional manifold. 2) The cohomology ring of the complement of a hyperplane arrangement (the Orlik-Solomon algebra).…

Let X be the quasi-projective symplectic surface that is given by the total space of the invertible sheaf O(-2) over the projective line. Let Hilb X be the family of Hilbert schemes of points on X. We give and prove a closed formula…

We study the eigenvalues and eigenfunctions of the Folland-Stein operator $\mathscr{L}_\alpha$ on some examples of 3-dimensional Heisenberg Bieberbach manifolds, that is, compact quotients $\Gamma\backslash\mathbb{H}$ of the Heisenberg…

We develop numerical algorithms for solving the Einstein equation on Calabi-Yau manifolds at arbitrary values of their complex structure and Kahler parameters. We show that Kahler geometry can be exploited for significant gains in…

We study modules over the algebroid stack $\W[\stx]$ of deformation quantization on a complex symplectic manifold $\stx$ and recall some results: construction of an algebra for $\star$-products, existence of (twisted) simple modules along…

The Hilbert scheme X^{[a]} of points on a complex manifold X is a compactification of the configuration space of a-element subsets of X. The integral cohomology of X^{[a]} is more subtle than the rational cohomology. In this paper, we…

Graded skew-commutative rings occur often in practice. Here are two examples: 1) The cohomology ring of a compact three-dimensional manifold. 2) The cohomology ring of the complement of a hyperplane arrangement (the Orlik-Solomon algebra).…

Considering the complex n-dimension Calabi-Yau homogeneous hyper-surfaces ${\cal H}_{n}$ and using algebraic geometry methods, we develop the crossed product algebra method, introduced by Berenstein et Leigh in hep-th/0105229, and build the…

We identify the twisted sectors of a compact simplicial toric variety. We do the same for a generic nondegenerate Calabi-Yau hypersurface of an $n$-dimensional simplicial Fano toric variety and then explicitly compute $h^{1,1}_{orb}$ and…

Riemannian Geometry, Topology and Dynamics permit to introduce partially defined holomorphic functions on the variety of representations of the fundamental group of a manifold. The functions we consider are the complex valued Ray-Singer…

We present our recent understanding on resolutions of Gorenstein orbifolds, which involves the finite group representation theory. We shall concern only the quotient singularity of hypersurface type. The abelian group $A_r(n)$ for $A$-type…

Let $(R, \mathcal{M})$ be a local ring over a field $k$ with $k = R/\mathcal M$ and $J$ an ideal in $R$ such that $A =R/J$ is an Artinian Gorenstein (AG) $k$-algebra. In 1989, A. Iarrobino introduced the symmetric decomposition of the…

Given any smooth toric surface S, we prove a SYM-HILB correspondence which relates the 3-point, degree zero, extended Gromov-Witten invariants of the n-fold symmetric product stack [Sym^n(S)] of S to the 3-point extremal Gromov-Witten…

This survey paper is devoted to Riemannian manifolds with special holonomy. To any Riemannian manifold of dimension n is associated a closed subgroup of SO(n), the holonomy group; this is one of the most basic invariants of the metric. A…