In algebraic geometry, a Fourier–Mukai transform ΦK is a functor between derived categories of coherent sheaves D(X) → D(Y) for schemes X and Y, which...

Fourier sine transform Fourier–Deligne transform Fourier–Mukai transform Fractional Fourier transform Indirect Fourier transform Integral transform Hankel...

coherent sheaves on X. Historically, this was the first use of the Fourier-Mukai transform and shows that the bounded derived category cannot necessarily...

Mukai (向井 茂, Mukai Shigeru, born 1953) is a Japanese mathematician at Kyoto University specializing in algebraic geometry. He introduced the Fourier–Mukai...

the Fourier transform, used in the area of harmonic analysis Fourier–Deligne transform Fourier–Mukai transform Fourier inversion theorem Fourier integral...

in Hyderabad and gave a talk Hyperkähler Manifolds and Sheaves. Fourier-Mukai transforms in Algebraic Geometry, Oxford Mathematical Monographs, 2006 Complex...

a complex of sheaves on X × Y {\displaystyle X\times Y} by the Fourier–Mukai transform. By contrast, there is an example of an exact functor from D b...

Leung, N.C., Yau, S.T. and Zaslow, E., 2000. From special lagrangian to hermitian-Yang-Mills via Fourier-Mukai transform. arXiv preprint math/0005118....

what had previously been a technical backwater. His results on Fourier–Mukai transforms solve many problems within algebraic geometry, and have been influential...

abelian variety and X ^ {\displaystyle {\hat {X}}} is its dual, the Fourier–Mukai transform with kernel P {\displaystyle {\mathcal {P}}} , the Poincare bundle...

the theory of Fourier–Mukai transforms. Varieties with equivalent derived categories of coherent sheaves are sometimes called Fourier–Mukai partners. Homotopy...

1070/IM1990v035n03ABEH000716, MR 1039961 Huybrechts, Daniel (2006), Fourier–Mukai transforms in algebraic geometry, Oxford University Press, ISBN 978-0199296866...

Springer-Verlag, ISBN 3-540-21290-6, MR 2093043 Huybrechts, Daniel (2006), Fourier–Mukai transforms in algebraic geometry, Oxford University Press, ISBN 978-0199296866...

curves to the abelian variety case. c. 1980 Mukai–Fourier transform: the Poincaré line bundle as Mukai–Fourier kernel induces an equivalence of the derived...

Zaslow, E., From special lagrangian to hermitian–Yang–Mills via Fourier–Mukai transform. Adv. Theor. Math. Phys. 4 (2000), no. 6, 1319–1341. Collins, T...

the two-torsion of A. An innovation in this area is to use the Mukai–Fourier transform. The goal of the theory is to prove results on the homogeneous...

Madhav Nori, A modified Hodge conjecture Justin Sawon, Twisted Fourier–Mukai transforms for holomorphic symplectic manifolds Wilfried Schmid, Automorphic...

Moduli of algebraic curves Griffith, Harris, p. 116, 117 Stichtenoth p.22 Mukai pp.295–297 Liu, Qing (2002), Algebraic Geometry and Arithmetic Curves, Oxford...

(1950–2022), a French chemist. IAU · 10144 10146 Mukaitadashi 1994 CV1 Tadashi Mukai (born 1945), a professor in the department of earth and planetary sciences...

Year Contributors Event 1981 Shigeru Mukai Mukai–Fourier transform 1982 Bob Walters Enriched categories with bicategories as a base 1983 Alexander Grothendieck...

s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing". Nature Photonics. 5 (6): 364–371. doi:10.1038/nphoton...