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math.AG2023
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…
math.AG2023
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…
math.AG2023
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…