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math.AG2025
Partial Cohomologically Complete Intersections via Hodge Theory
Qianyu Chen, Bradley Dirks, Sebastian Olano
We introduce an invariant associated to any complex algebraic variety , which for varieties with isolated singularities measures the failure of dual Kodaira-Akizuki-Nakan…
math.AG2025
Hirzebruch-Milnor classes of local complete intersections, minimal exponent, and applications to higher singularities
Bradley Dirks, Laurenţiu Maxim, Sebastián Olano
In this paper we use the deformation to the normal cone and the corresponding Verdier-Saito specialization to define and study (spectral) Hirzebruch-Milnor type homology characteri…
math.AG2025
A Hodge Theoretic generalization of -Homology Manifolds I: General Case
Bradley Dirks, Sebastian Olano, Debaditya Raychaudhury
We study a natural Hodge-theoretic generalization of rational (or -)homology manifolds through an invariant $\HRH(Z)$ attached to a complex algebraic variety . The d…