719 citations · 3.5k across the 84 of their papers we have counts for
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The arithmetic-geometric mean and isogenies for curves of higher genus
Ron Donagi, Ron Livne
Computation of Gauss's arithmetic-geometric mean involves iteration of a simple step, whose algebro-geometric interpretation is the construction of an elliptic curve isogenous to a…
Seiberg-Witten integrable systems
Ron Y. Donagi
This is a survey of the work of Seiberg and Witten on 4-dimensional N=2 supersymmetric Yang-Mills theory and of some of its recent extensions, written for mathematicians. The point…
Principal bundles on elliptic fibrations
Ron Y. Donagi
A central role in recent investigations of the duality of F-theory and heterotic strings is played by the moduli of principal bundles, with various structure groups G, over an elli…
Spectral curves, algebraically completely integrable Hamiltonian systems, and moduli of bundles
Ron Donagi, Eyal Markman
This is the expanded text of a series of CIME lectures. We present an algebro-geometric approach to integrable systems, starting with those which can be described in terms of spect…
Spectral Covers
Ron Donagi
This is a survey of various results about spectral covers and their relationship to Higgs bundles. To a G-principal Higgs bundle on a variety S corresponds a cameral cover \widetil…
A Non-Linear Deformation of the Hitchin Dynamical System
Ron Donagi, Lawrence Ein, Robert Lazarsfeld
Mukai's space, parametrizing simple sheaves on a K3 surface S whose numerical invariants are those of a line bundle on a curve C in S, is interpreted as a deformation of Hitchin's…
Cubics, Integrable Systems, and Calabi-Yau Threefolds
Ron Donagi, Eyal Markman
In this work we construct an analytically completely integrable Hamiltonian system which is canonically associated to any family of Calabi-Yau threefolds. The base of this system i…
Theta Functions for $\SL(n)$ versus $\GL(n)$
Ron Donagi, Loring W. Tu
Over a smooth complex projective curve of genus let $\M (n,d)$ be the moduli space of semistable bundles of rank and degree on , and $\SM (n,L)$, the moduli spac…