3 problems

Batyrev's conjecture. The universal torsor over any del Pezzo surface admits an embedding into the homogeneous space defined by the orbit of the highest weight vector of the repres…

Let $G_r$ be the simply connected semisimple group of type $R_r$, let $H_r\subset G_r$ be a fixed maximal torus, and let $P_r\subset G_r$ be the maximal parabolic subgroup defined…

Let $X$ be a projective Calabi–Yau manifold, meaning that its canonical bundle is torsion and … and let $\mathcal U$ be a universal torsor for $X$. Lift conjecture. The action of…