2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101115Let $G$ be a connected affine algebraic group and $X$ a regular $G$-variety (in the sense of Bifet-De Concini-Procesi) with open orbit $G/H$ and boundary divisor $D$. We show the vanishing of the $G$-equivariant Chern classes of the bundle of differential forms on $X$ with logarithmic poles along $D$, in degrees larger than $\dim(X) - \rk(G) + \rk(H)$. Our motivation comes from Gieseker's degeneration method to prove the Newstead-Ramanan conjecture on the vanishing of the top Chern classes of the moduli space of stable vector bundles on a curve.8 pages. Corollary 2.6 added, typos corrected. To appear in Asian Journal of MathematicsAlgebraic Geometry14H60, 14L30, 14M17, 55N91text