Newton Polytopes ans Irreducibility

Student: Zhizhin Andrei

Educational Programme: Mathematics (Bachelor)

Final Grade: 10

Year of Graduation: 2024

We develop an approach to study the irreducibility of generic complete intersections in the algebraic torus defined by equations with fixed monomials and fixed linear relations on coefficients. Using our approach we generalize the irreducibility theorems of Khovanskii from \cite{Khovanskii2016} to arbitrary algebraically closed field. Also we get a combinatorial sufficient conditions for irreducibility of engineered complete intersections (introduced in \cite{Esterov2024}). As an application we give combinatorial condition for irreducibility for some critical loci: $f = f'_x = 0$, $f'_x = f'_y = 0$, $f = f'_x = f'_{xx} = 0$.

Full text (added June 10, 2024)

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