8 citations · 43 across the 27 of their papers we have counts for
27 papers
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…
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})…
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…
Matrix factorization for quasi-homogeneous singularities
Ananyo Dan, Agustín Romano-Velázquez
Given an isolated, quasi-homogeneous singularity we prove that there is a group isomorphism between the group of rank one reflexive sheaves on and the free abelian group ge…
Failure of Lefschetz hyperplane theorem
Ananyo Dan
In this article, we give a counterexample to the Lefschetz hyperplane theorem for non-singular quasi-projective varieties. A classical result of Hamm-Lê shows that Lefschetz hyperp…
Mumford Tate groups and the Hodge conjecture
Ananyo Dan, Inder Kaur
In this article we study the (cohomological) Hodge conjecture for singular varieties. We prove the conjecture for simple normal crossing varieties that can be embedded in a family…