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math.AG2026

Spectral and Logarithmic Atiyah Classes for Higgs Bundles

Pradip Kumar, Sai Rasmi Ranjan Mohanty, Savita Rani +1

For a regular semisimple Higgs bundle with a smooth spectral curve, we prove that, over the \etale\ locus, the Atiyah class of the underlying bundle is induced by the Atiyah class…

math.AG2026

Equivariant Chevalley, Giambelli, and Monk Formulae for the Peterson Variety

Rebecca Goldin, Rahul Singh

We present a formula for the Poincaré dual in the flag manifold of the equivariant fundamental class of any regular nilpotent or regular semisimple Hessenberg variety as a polynom…

math.AG2025

Counting Parabolic Principal G-bundles with Nilpotent Sections over

Rahul Singh

Let be a split connected reductive group over and let be the projective line over . Firstly, we give an explicit formula for the num…

math.AG2024

Positivity of Peterson Schubert Calculus

Rebecca Goldin, Leonardo Mihalcea, Rahul Singh

The Peterson variety is a subvariety of the flag manifold equipped with an action of a one-dimensional torus, and a torus invariant paving by affine cells, called Peterson ce…