2001/03/22 by Balázs Szendröi, Balazs Szendroi, Szendroi, Balazs
Mathematics · Medicine · Physics and Astronomy · #Advanced Differential Geometry Research #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Ophthalmology and Eye Disorders #hep-th #math-ph #math.AG #math.MP
paper · pdf · doi:10.48550/arxiv.math/0103137
Approx. 20 pages LaTeX. One reference added
openalex publication_date 2001/03/22 · arxiv created 2001/03/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Assuming the standard framework of mirror symmetry, a conjecture is formulated describing how the diffeomorphism group of a Calabi-Yau manifold Y should act by families of Fourier-Mukai transforms over the complex moduli space of the mirror X. The conjecture generalizes a proposal of Kontsevich relating monodromy transformations and self-equivalences. Supporting evidence is given in the case of elliptic curves, lattice-polarized K3 surfaces and Calabi-Yau threefolds. A relation to the global Torelli problem is discussed.