3 citations · 6 across the 5 of their papers we have counts for
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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…
Semi-regular varieties and variational Hodge conjecture
Ananyo Dan, Inder Kaur
We know that semi-regular sub-varieties satisfy the variational Hodge conjecture i.e., given a family of smooth projective varieties , a special fiber $\mathca…
Hodge locus and Brill-Noether type locus
Indranil Biswas, Ananyo Dan
Given a family $π:\mc{X} \rightarrow B$ of smooth projective varieties, a closed fiber $\mc{X}_o$ and an invertible sheaf $\mc{L}$ on $\mc{X}_o$, we compare the Hodge locus in …
Non-reduced components of the Noether-Lefschetz locus
Ananyo Dan
For a fixed integer , the Noether-Lefschetz locus parametrizes smooth degree complex hypersurfaces in with Picard number greater than . There are inf…