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Genus 4 Supermoduli Space Is Not Projected
Ron Donagi, Simone Noja
The supermoduli stack , parametrizing smooth unpunctured super Riemann surfaces of genus , is known to be non-projected for . We extend this result to…
Supermoduli Space with Ramond punctures is not projected
Ron Donagi, Nadia Ott
The supermoduli space is not projected for all .
Hodge classes on the moduli space of W(E_6)-covers and the geometry of A_6
Valery Alexeev, Ron Donagi, Gavril Farkas +2
In previous work we showed that the Hurwitz space of W(E_6)-covers of the projective line branched over 24 points dominates via the Prym-Tyurin map the moduli space A_6 of principa…
Folding of Hitchin systems and crepant resolutions
Florian Beck, Ron Donagi, Katrin Wendland
Folding of ADE-Dynkin diagrams according to graph automorphisms yields irreducible Dynkin diagrams of ABCDEFG-types. This folding procedure allows to trace back the properties of t…
Parabolic Hecke eigensheaves
Ron Donagi, Tony Pantev
We study the Geometric Langlands Conjecture (GLC) for rank two flat bundles on the projective line with tame ramification at five points $\{p_{1}, p_{2}, p_{3}, p_{4}, p_{5} \}…
On the global moduli of Calabi-Yau threefolds
Ron Donagi, Mark Macerato, Eric Sharpe
In this note we initiate a program to obtain global descriptions of Calabi-Yau moduli spaces, to calculate their Picard group, and to identify within that group the Hodge line bund…
Direct Images in Non Abelian Hodge Theory
R. Donagi, T. Pantev, C. Simpson
In this paper we explain how non-abelian Hodge theory allows one to compute the cohomology or middle perversity higher direct images of harmonic bundles and twistor D-modules…
ADE Transform
Ron Donagi, Martijn Wijnholt
There is a beautiful correspondence between configurations of lines on a rational surface and tautological bundles over that surface. We extend this correspondence to families, by…
The uniformization of the moduli space of principally polarized abelian 6-folds
Valery Alexeev, Ron Donagi, Gavril Farkas +2
Starting from a beautiful idea of Kanev, we construct a uniformization of the moduli space A_6 of principally polarized abelian 6-folds in terms of curves and monodromy data. We sh…
A Mathematical Theory of Quantum Sheaf Cohomology
Ron Donagi, Josh Guffin, Sheldon Katz +1
The purpose of this paper is to present a mathematical theory of the half-twisted gauged linear sigma model and its correlation functions that agrees with and extends resul…
On a class of non-simply connected Calabi-Yau threefolds
Vincent Bouchard, Ron Donagi
We obtain a detailed classification for a class of non-simply connected Calabi-Yau threefolds which are of potential interest for a wide range of problems in string phenomenology.…
Langlands duality for Hitchin systems
Ron Donagi, Tony Pantev
We show that the Hitchin integrable system for a simple complex Lie group is dual to the Hitchin system for the Langlands dual group $\lan{G}$. In particular, the general fiber…
Abelian Varieties with Quaternion Multiplication
Ron Donagi, Ron Livné
In this article we use a Prym construction to study low dimensional abelian varieties with an action of the quaternion group. In special cases we describe the Shimura variety param…
Torus fibrations, gerbes, and duality
Ron Donagi, Tony Pantev
Let X be a smooth elliptic fibration over a smooth base B. Under mild assumptions, we establish a Fourier-Mukai equivalence between the derived categories of two objects, each of w…
Surface bundles over surfaces of small genus
Jim Bryan, Ron Donagi
We construct examples of non-isotrivial algebraic families of smooth complex projective curves over a curve of genus 2. This solves a problem from Kirby's list of problems in low-d…
Spectral involutions on rational elliptic surfaces
Ron Donagi, Burt Ovrut, Tony Pantev +1
In this paper we describe a four dimensional family of special rational elliptic surfaces admitting an involution with isolated fixed points. For each surface in this family we cal…
Standard-model bundles
Ron Donagi, Burt Ovrut, Tony Pantev +1
We describe a family of genus one fibered Calabi-Yau threefolds with fundamental group . On each Calabi-Yau in the family we exhibit a positive dimensional famil…
The gerbe of Higgs bundles
R. Donagi, D. Gaitsgory
The purpose of this work is to describe the (category of) Higgs bundles on a complex scheme X having a given cameral cover X~. We show that this category is a T_{X~}-gerbe, where T…
G-bundles on Abelian surfaces, hyperkahler manifolds, and stringy Hodge numbers
Jim Bryan, Ron Donagi, Naichung Conan Leung
We study the moduli space M(G,A) of flat G-bundles on an Abelian surface A, where G is a compact, simple, simply connected, connected Lie group. Equivalently, M(G,A) is the (coarse…