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math.AG2025
Hodge Conjecture via Singular Varieties
Ananyo Dan, Inder Kaur
In this article we study the cohomological and homological (due to Jannsen) Hodge conjecture for singular varieties. The motivation for studying singular varieties comes from the f…
math.AG2025
Extended operational Chow group and Lefschetz (1,1)-theorem
Ananyo Dan, Inder Kaur
Let be a singular, projective variety. For every , is equipped with a mixed Hodge structure. The elements of $\mathrm{Gr}^W_{2p}H^{2p}(X,\mathbb{Q})…
math.AG2025
Cohen-Macaulay modules and the Bondal-Orlov conjecture
Ananyo Dan, Yirui Xiong
Most of the known examples of derived categories of small resolutions arise as the derived category of the endormorphism algebra of tilting bundles or complexes. Given two resoluti…