Rahul Ajit

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math.AG2026

Bertini theorems for Hilbert-Samuel multiplicity over finite fields

Rahul Ajit, Matthew Bertucci

Let $X$ be a quasiprojective subscheme of $P_{F_{q}}^{n}$ . We prove a Bertini theorem for Hilbert--Samuel multiplicity of $X$ ; that is, there exists a positive-densit…

math.AG2026

$F$ -jumping numbers can be irrational

Rahul Ajit

Let $k$ be an $F$ -finite and infinite field of characteristic $p > 2$ . We show, there exist infinitely many $F$ -finite local domains $(R, m)$ which are not $Q$ -Gor…

math.AG2025

On a Grauert-Riemenschneider vanishing theorem in dimension 3

Rahul Ajit

Suppose $R$ is an excellent ring of dimension $3$ and has rational singularities. Let $π : X ⟶ Spec R$ be a blow-up and $ϕ : W ⟶ X$ be any proje…

math.AG2025

Multiplier Modules of extended Rees algebras

Rahul Ajit

Given a local ring $(R, m)$ and an ideal $a$ of positive height, we give a way of computing multiplier module $J (ω_{T}, t^{- λ})$ for the extended Rees algeb…

Bertini theorems for Hilbert-Samuel multiplicity over finite fields

F-jumping numbers can be irrational

On a Grauert-Riemenschneider vanishing theorem in dimension 3

Multiplier Modules of extended Rees algebras

$F$ -jumping numbers can be irrational