Related papers: Harmonic theta series and the Kodaira dimension of…

We consider a heterotic version of six-dimensional Kodaira-Spencer gravity derived from the heterotic superpotential. We compute the one-loop partition function and find it can be expressed as a product of holomorphic Ray-Singer torsions.…

We consider the space of Siegel modular forms of genus $g$ of weight two relative to the main congruence subgroup of level 2 and to Igusa's group $\Gamma_g(4, 8)$ and $\Gamma_g(2,4)$.One of the main results of this paper is that in the case…

We study canonical bases for spaces of weakly holomorphic modular forms of level 4 and weights in $\mathbb{Z}+\frac{1}{2}$ and show that almost all modular forms in these bases have the property that many of their zeros in a fundamental…

We chart the classical moduli space of heterotic strings with broken supersymmetry a la Scherk-Schwarz and gauge group rank reduced by 8 in eight dimensions. This space consists of four connected components, each with its own characteristic…

The zeta-function of a complex variety is a power series whose nth coefficient is the nth symmetric power of the variety, viewed as an element in the Grothendieck ring of complex varieties. We prove that the zeta-function of a surface is…

The space of toroidal automorphic forms was introduced by Zagier in 1979. Let $F$ be a global field. An automorphic form on $\GL(2)$ is toroidal if it has vanishing constant Fourier coefficients along all embedded non-split tori. The…

We prove that the moduli space ${\mathcal A}_{g,\Gamma_0(p)}\otimes \bar {\mathbb F}_p$ of principally polarized abelian varieties of dimension $g$ with a $\Gamma_0(p)$-level structure in characteristic $p$ has $2^g$ irreducible…

The isometry between the type IV$_6$ and the type II$_4$ hermitian symmetric domains suggests a possible relation between suitable moduli spaces of K3 surfaces of Picard rank $14$ and of polarised abelian $8$-folds with totally definite…

This is a survey on the various notions of Kodaira dimension in low dimensional topology. The focus is on progress after the 2006 survey [78].

We investigate the behaviour of orthogonal non-holomorphic Eisenstein series at their harmonic points by using theta lifts. In the case of singular weight, we show that the orthogonal non-holomorphic Eisenstein series that can be written as…

Hecke expected that an explicit set of theta series obtained from maximal orders of the definite quaternion algebra over Q which is ramified at a prime N will be a basis of the space of holomorphic modular forms of weight 2 and level N.…

There are a number of fundamental results in the study of holomorphic function theory associated to the discrete group PSL(2,Z) including the following statements: The ring of holomorphic modular forms is generated by the holomorphic…

We continue the program of classification of normal Q-acyclic surfaces defined over the field of complex numbers, so-called 'Q-homology planes'. Here we show that if a Q-homology plane has negative Kodaira dimension then its smooth locus is…

Gravitational theta-sectors are investigated in spatially locally homogeneous cosmological models with flat closed spatial surfaces in 2+1 and 3+1 spacetime dimensions. The metric ansatz is kept in its most general form compatible with…

We study the birational geometry of some moduli spaces of abelian varieties with extra structure: in particular, with a symmetric theta structure and an odd theta characteristic. For a $(d_1,d_2)$-polarized abelian surface, we show how the…

A complex algebraic surface $S$ is a $\mathbb{Q}$-homology plane if $H_{i}(S,\mathbb{Q})=0$ for $i>0$. The Negativity Conjecture of Palka asserts that $\kappa(K_{X}+\tfrac{1}{2}D)=-\infty$, where $(X,D)$ is a log smooth completion of $S$.…

The primal cohomology $\mathbb{K}_\mathbb{Q}$ of the theta divisor $\Theta$ of a principally polarized abelian fivefold (ppav) is the direct sum of its invariant and anti-invariant parts $\mathbb{K}_\mathbb{Q}^{+1}$, resp.…

Let $f:X@>>>\Bbb P^1$ be a fibered surface with fibers of genus g>1. If f is semistable and non isotrivial we prove that X of non negative Kodaira dimension implies that the number s of singular fibers is at least 5. Information about the…

Our aim is to derive the effective action in four dimensions resulting by reducing dimensionally the ten-dimensional ${\cal N}=1$ heterotic supergravity coupled to ${\cal N}=1$ super Yang-Mills over manifolds admitting a nearly-K\"{a}hler…

The space of abelian functions of a principally polarized abelian variety J is studied as a module over the ring D of global holomorphic differential operators on J. We construct a D-free resolution in case the theta divisor is…