We are grateful to A. Beauville, S. Bloch, I. Dolgachev, G. Kapustka, D. Markushevich, Yu. Prokhorov, and E. Tevelev, for useful discussions. We also thank the referee for valuable remarks. This paper was written during the Cheltov's stay at the Max Planck Institute for Mathematics in 2017. He would like to thank the institute for the excellent working conditions. All authors were partially supported by the HSE University Basic Research Program, Russian Academic Excellence Project "5-100". Kuznetsov and Shramov were also supported by RFBR grants 15-01-02164 and 15-01-02158. Shramov was also supported by Young Russian Mathematics award.