arXiv subjects

Priyankur Chaudhuri

Publications and source records attributed to Priyankur Chaudhuri.

8 recordsLinked to original sources

arXiv2025

Log Canonical Minimal Model Program for corank one foliations on Threefolds

If $(X, \mcF, \D)$ is a projective rank two foliated log canonical triple such that $(X,B)$ is klt for some $0 \leq B \leq \D$, we show that we can run a $(K_\mcF +Δ)$-MMP and any such MMP terminates with either a minimal model or Mori fiber space. Next, we establish a Bertini type lemma and adjunction for generalized foliated quadruples. Using these, we extend the full log canonical MMP to the setting of rank two NQC generalized foliated quadruples. Finally, we apply the generalized MMP to study the relation between different minimal models, namely, any two minimal models of a given foliated log canonical triple can be connected by a sequence of flops and in the boundary polarized case, the minimal models are good and only finitely many in number.

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arXiv2023

A basepoint free theorem for algebraically integrable foliations

We show that if $\mathcal{F}$ is an algebraically integrable foliation on a $\mathbb{Q}$-factorial normal projective variety $X$, $ A, B \geq 0$ are $\mathbb{Q}$-divisors on $X$ with $A$ ample such that $(\mathcal{F}, B)$ is foliated dlt and $K_{\mathcal{F}}+ A+B$ is nef, then $K_{\mathcal{F}}+A+B$ is semiample. We also provide some applications of this and related results such as contraction theorem for F-dlt pairs and a special case of the b-semiampleness conjecture.

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arXiv2023

Flops and minimal models for generalized pairs

We show that given any two minimal models of a generalized lc pair, there exist small birational models which are connected by a sequence of symmetric flops. We also present some applications.

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arXiv2022

Semiampleness for generalized pairs

We prove that if $(X, B+\mathbf{M})$ is a generalized klt pair with $K_X+B+\mathbf{M}_X$ nef and abundant, then $K_X+B+\mathbf{M}_X$ is semiample. More generally, we prove a generalized basepoint free theorem for generalized klt pairs.

math.AG↗

arXiv2022

Nef and abundant divisors, semiampleness and canonical bundle formula

In this paper, we use canonical bundle formulas to prove some generalizations of an old theorem of Kawamata on the semiampleness of nef and abundant log canonical divisors. In particular, we show that for klt pairs $(X,B)$ with $K_X+B$ effective, $L \in Pic (X)$ nef, nefness and abundance of $K_X+B+L$ implies semiampleness. This essentially generalizes Kawamata's theorem to the setting of generalized abundance.

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arXiv2022

An inductive approach to generalized abundance using nef reduction

We use the canonical bundle formula for parabolic fibrations to give an inductive approach to the generalized abundance conjecture using nef reduction. In particular, we observe that generalized abundance holds for a klt pair $(X,B)$ if the nef dimension $n(K_X+B+L)=2$ and $K_X+B \geq 0$ or $n(K_X+B+L)=3$ and $κ(K_X+B )>0$.

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arXiv2021

Strictly nef divisors and some remarks on a conjecture of Serrano

Serrrano's Conjecture says that if $L$ is a strictly nef line bundle on a smooth projective variety $X$, then $K_X+tL$ is ample for $ t > dim X+1$. In this paper I will prove a few cases of this conjecture. I will also prove a generalized version of this conjecture (due to Campana, Chen and Peternell) for surfaces. In the last section, assuming the SHGH conjecture, I will give a series of examples of strictly nef non ample divisors on surfaces of arbitary Kodaira dimension.

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arXiv2020

Strictly nef Bundles

In this short note we will show that every homogeneous strictly nef vector bundle on a complex flag variety is ample. Following this, we consider whether ampleness of a bundle on an abelian variety can be tested on curves.

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