Michael Chitayat

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20192026

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math.AG2026

Borel subgroups of the automorphism group of an affine variety

Michael Chitayat, Daniel Daigle, Andriy Regeta

We study Borel subgroups of the automorphism group of an affine variety X and their associated Lie algebras. We prove a bijective correspondence between the set of Borel subgroups…

math.AG2026

A Survey on Pham-Brieskorn Varieties

Michael Chitayat

This is a survey on Pham-Brieskorn varieties and their various properties, targeted for graduate students.

math.AG2026

The Isomorphism Classes of the Surfaces $x_{1}^{a_{1}} + x_{2}^{a_{2}} + x_{3}^{a_{3}} + 1 = 0$

Michael Chitayat, Buddhadev Hajra

Let $f = x_{1}^{a_{1}} + x_{2}^{a_{2}} + x_{3}^{a_{3}} + 1 \in C [x_{1}, x_{2}, x_{3}]$ and let $g = y_{1}^{b_{1}} + y_{2}^{b_{2}} + y_{3}^{b_{3}} + 1 \in C [y_{1}, y_{2}, y_{3}]$ where $a_1,a_2,a_3,b_1,b…

math.AG2023

The Rigid Pham-Brieskorn Threefolds

Michael Chitayat, Adrien Dubouloz

We show that a $3$ -dimensional Pham-Brieskorn hypersurface ${X_{0}^{a_{0}} + X_{1}^{a_{1}} + X_{2}^{a_{2}} + X_{3}^{a_{3}} = 0}$ in $A^{4}$ such that $min {a_{0}, a_{1}, a_{2}, a_{3}} \geq 2$ a…

math.AG2023

Rationality of weighted hypersurfaces of special degree

Michael Chitayat

Let $X \subset P (w_{0}, w_{1}, w_{2}, w_{3})$ be a quasismooth well-formed weighted projective hypersurface and let $L = l c m (w_{0}, w_{1}, w_{2}, w_{3})$ . We characterize when $X$ is rationa…

math.AG2021

Locally nilpotent derivations of graded integral domains and cylindricity

Michael Chitayat, Daniel Daigle

Let B be a commutative $Z$ -graded domain of characteristic zero. An element f of B is said to be cylindrical if it is nonzero, homogeneous of nonzero degree, and such that…

Borel subgroups of the automorphism group of an affine variety

A Survey on Pham-Brieskorn Varieties

The Isomorphism Classes of the Surfaces x1a1​​+x2a2​​+x3a3​​+1=0

The Rigid Pham-Brieskorn Threefolds

Rationality of weighted hypersurfaces of special degree

Locally nilpotent derivations of graded integral domains and cylindricity

The Isomorphism Classes of the Surfaces $x_{1}^{a_{1}} + x_{2}^{a_{2}} + x_{3}^{a_{3}} + 1 = 0$