6 citations · 9 across the 6 of their papers we have counts for
7 papers
Rank Bounds and PIT for circuits via a non-linear Edelstein-Kelly theorem
Abhibhav Garg, Rafael Oliveira, Akash Kumar Sengupta
We prove a non-linear Edelstein-Kelly theorem for polynomials of constant degree, fully settling a stronger form of Conjecture 30 in Gupta (2014), and generalizing the main result…
Strong Algebras and Radical Sylvester-Gallai Configurations
Rafael Oliveira, Akash Kumar Sengupta
In this paper, we prove the following non-linear generalization of the classical Sylvester-Gallai theorem. Let be an algebraically closed field of characteristic ,…
Robust Radical Sylvester-Gallai Theorem for Quadratics
Abhibhav Garg, Rafael Oliveira, Akash Sengupta
We prove a robust generalization of a Sylvester-Gallai type theorem for quadratic polynomials, generalizing the result in [S'20]. More precisely, given a parameter an…
Geometric consistency of Manin's Conjecture
Brian Lehmann, Akash Kumar Sengupta, Sho Tanimoto
We conjecture that the exceptional set in Manin's Conjecture has an explicit geometric description. Our proposal includes the rational point contributions from any generically fini…
Manin's Conjecture and the Fujita invariant of finite covers
Akash Kumar Sengupta
We prove a conjecture of Lehmann-Tanimoto about the behaviour of the Fujita invariant (or -constant appearing in Manin's conjecture) under pull-back to generically finite covers…
Manin's b-constant in families
Akash Kumar Sengupta
We show that the -constant (appearing in Manin's conjecture) is constant on very general fibers of a family of algebraic varieties. If the fibers of the family are uniruled, the…
Counterexamples to Mercat's Conjecture
Akash Kumar Sengupta
For any n>3, we provide examples of curves lying on K3 surfaces and vector bundles on those curves which invalidate Mercat's conjecture for rank n bundles.