By Kai Behrend, Barbara Fantechi (auth.), Yuri Tschinkel, Yuri Zarhin (eds.)

ISBN-10: 0817647449

ISBN-13: 9780817647445

Algebra, mathematics, and Geometry: In Honor of Yu. I. Manin comprises invited expository and examine articles on new advancements bobbing up from Manin’s remarkable contributions to arithmetic.

Contributors within the first quantity include:

okay. Behrend, V.G. Berkovich, J.-B. Bost, P. Bressler, D. Calaque, J.F. Carlson, A. Chambert-Loir, E. Colombo, A. Connes, C. Consani, A. Da˛browski, C. Deninger, I.V. Dolgachev, S.K. Donaldson, T. Ekedahl, A.-S. Elsenhans, B. Enriquez, P. Etingof, B. Fantechi, V.V. Fock, E.M. Friedlander, B. van Geemen, G. van der Geer, E. Getzler, A.B. Goncharov, V.A. Iskovskikh, J. Jahnel, M. Kapranov, E. Looijenga, M. Marcolli, B. Tsygan, E. Vasserot, M. Wodzicki.

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Additional info for Algebra, Arithmetic, and Geometry: Volume I: In Honor of Yu. I. Manin

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As generators in degree −1, we may take the basic vector fields of a coordinate system for C. We choose this coordinate system such that M is cut out by a subset of the coordinates. Then, if we plug in generators of degree −1 for both X and Y in formula (4), every term vanishes. Also, if we plug in terms of degree 0 for both X and Y , both sides of (4) vanish for degree reasons. , a regular function on C. Hence we need to prove that for all X ∈ TC and g ∈ OC we have X(g)|M − ρ(X)|M g|M = {(t − s )X, g} − t{X, g} .

1996 [186] Quantum cohomology of a product (with M. Kontsevich and Appendix by R. Kaufmann). Inv. , 124, f. 1–3 (1996), 313–339 (Remmert’s Festschrift). [187] Quantum groups and algebraic groups in non–commutative geometry. In: Quantum Groups and their Applications in Physics, ed. by L. Castellani and J. Wess, Proc. of the Int. School of Physics “Enrico Fermi”, IOS Press, (1996), 347–359. [188] Distribution of rational points on Fano varieties. Publ. RIMS Kokyuroku 958, Analytic Number Theory, (1996), 98–104.

We may assume that the leaves of our Lagrangian foliation of S are transverse to the two Lagrangians L and M whose intersection we wish to study. Then L and M turn into the graphs of 1-forms on N . The Lagrangian condition implies that these 1-forms on N are closed. Without loss of generality, we may assume that one of these 1-forms is the zero section of ΩN and hence identify M with N . By making M = N smaller if necessary, we may assume that the closed 1-form defined by L is exact. Then L is the graph of the 1-form df , for a holomorphic function f on M .

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Algebra, Arithmetic, and Geometry: Volume I: In Honor of Yu. I. Manin by Kai Behrend, Barbara Fantechi (auth.), Yuri Tschinkel, Yuri Zarhin (eds.)

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