Restriction of tangent bundle and semistability

摘要

Let G be a simple linear algebraic group defined over C and P ∪ G a maximal proper parabolic subgroup such that m:= dim_CG/P ≥ 5. Let i:Z_1∩ Z_2 {right arrow, hooked} G/P be a smooth complete intersection such that degree Z_i ≥ (m-1) ·index (G/P)/m, i=1, 2. Then the vector bundle i*T(G/P) → Z_1 ∩ Z_2 is semistable.