Let X be a nonsingular complex projective toric variety. We address the question of semi-stability as well stability for tangent bundle T X. In particular, complete answer is given when Fano variety dimension four with Picard number at most two, complementing earlier work Nakagawa (Tohoku. Math. J. 45 (1993) 297–310; 46 (1994) 125–133). also give an infinite set examples varieties which TX unst...

Abstract Let X be a compact, Kähler, Calabi‐Yau threefold and suppose , for is conifold transition obtained by contracting finitely many disjoint curves in then smoothing the resulting ordinary double point singularities. We show that, sufficiently small, tangent bundle admits Hermitian‐Yang‐Mills metric with respect to conformally balanced metrics constructed Fu‐Li‐Yau. Furthermore, we describ...