Geodesic
Hirzebruch Functional Equations and Krichever Complex Genera
Matematičeskie zametki, Tome 103 (2018) no. 2, pp. 236-247.

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As is well known, the two-parameter Todd genus and the elliptic functions of level $d$ define $n$-multiplicative Hirzebruch genera if $d$ divides $n+ 1$. Both cases are special cases of the Krichever genera defined by the Baker–Akhiezer function. In the present paper, the inverse problem is solved. Namely, it is proved that only these properties define $n$-multiplicative Hirzebruch genera among all Krichever genera for all $n$.
Mots-clés : Hirzebruch genus
Keywords: elliptic function, functional equation. 
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I. V. Netay. Hirzebruch Functional Equations and Krichever Complex Genera. Matematičeskie zametki, Tome 103 (2018) no. 2, pp. 236-247. http://geodesic.mathdoc.fr/item/MZM_2018_103_2_a6/

[1] V. M. Bukhshtaber, I. V. Netai, “Funktsionalnoe uravnenie Khirtsebrukha i ellipticheskie funktsii urovnya $d$”, Funkts. analiz i ego pril., 49:4 (2015), 1–17 | DOI

[2] V. M. Buchstaber, T. E. Panov, N. Ray, “Toric genera”, Int. Math. Res. Not. IMRN, 2010:16 (2010), 3207–3262 | MR | Zbl

[3] V. M. Buchstaber, T. E. Panov, Toric Topology, Math. Surveys Monogr., 204, Amer. Math. Soc., Providence, RI, 2015 | MR | Zbl

[4] I. M. Krichever, “Formalnye gruppy i formula Ati–Khirtsebrukha”, Izv. AN SSSR. Ser. matem., 38:6 (1974), 1289–1304 | MR | Zbl

[5] Oleg R. Musin, “On rigid Hirzebruch genera”, Mosc. Math. J., 11:1 (2011), 139–147 | MR | Zbl

[6] F. Hirzebruch, Th. Berger, R. Jung, Manifolds and Modular Forms, Friedr. Vieweg Sohn, Braunschweig, 1992 | MR | Zbl

[7] F. Hirzebruch, “Elliptic genera of level $N$ for complex manifolds”, Differential Geometrical Methods in Theoretical Physics, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 250, Kluwer Acad. Publ., Dordrecht, 1988, 37–63 | DOI | MR | Zbl

[8] V. M. Bukhshtaber, E. Yu. Netai, “$\mathbb{C}P(2)$-multiplikativnye rody Khirtsebrukha i ellipticheskie kogomologii”, UMN, 69:4 (418) (2014), 181–182 | DOI | MR | Zbl

[9] V. M. Bukhshtaber, E. Yu. Bunkova, “Mnogoobraziya reshenii funktsionalnykh uravnenii Khirtsebrukha”, Sovremennye problemy matematiki, mekhaniki i matematicheskoi fiziki, Tr. MIAN, 290, MAIK, M., 2015, 136–148 | DOI

[10] I. M. Krichever, “Obobschennye ellipticheskie rody i funktsii Beikera–Akhiezera”, Matem. zametki, 47:2 (1990), 34–45 | MR | Zbl

[11] I. M. Krichever, “Ellipticheskie resheniya uravneniya Kadomtseva–Petviashvili i integriruemye sistemy chastits”, Funkts. analiz i ego pril., 14:4 (1980), 45–54 | MR | Zbl

[12] U. Fulton, Tablitsy Yunga i ikh prilozheniya k teorii predstavlenii i geometrii, MNTsMO, M., 2006