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Algebraic Geometry

The geometry of solution sets of polynomial equations, studied through the algebra of the rings that define them.

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3 works
People
3 researchers

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Researchers in Algebraic Geometry

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@bogdan_zavyalov

I am currently an assistant professor at the University of Maryland. Previously, I was a postdoc at the Princeton University (2024-2025), a postdoc at the Institute for Advanced Study (2022-2025), and a postdoc at Max Planck Institute (2021-2022). Before that, I was a graduate student at Stanford University.

@sean_cotner

NSF Research Fellow and postdoc at the University of Bonn. Previously an NSF Research Fellow and Postdoctoral Assistant Professor at the University of Michigan, and before that a graduate student at Stanford, advised by Brian Conrad. Interested in arithmetic geometry, algebraic groups (broadly construed), and integral questions connected to the local Langlands program.

Артём Алексеевич Авилов — доцент факультета математики НИУ ВШЭ и научный сотрудник Лаборатории алгебраической геометрии и её приложений (с 2017 года). Работает в Высшей школе экономики с 2012 года. Окончил механико-математический факультет МГУ имени М. В. Ломоносова (2012). Кандидат физико-математических наук (2016), диссертация «Автоморфизмы алгебраических многообразий и минимальные модели». В НИУ ВШЭ читает курсы по алгебраической геометрии — в 2026/27 учебном году «Алгебраические поверхности» и «Введение в теорию схем»; в Независимом московском университете осенью 2026 года читает курс «Алгебра-1».

Works in Algebraic Geometry

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The torsion component of the Picard scheme

2026OtherBogdan Zavyalov

Every finite flat commutative group scheme over a noetherian local ring is the torsion component of the Picard scheme of a smooth projective scheme with 3-dimensional fibers, built as a quotient of a complete intersection. An application: Hodge numbers that jump in a smooth projective family.
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A curiosity: “supersmooth” varieties

2026TheorySean Cotner

A rigidity condition on schemes, strictly stronger than smoothness, introduced with examples and a look at where it fails to be geometric — no known application, just a curiosity.
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An example of a non-reduced Picard scheme

2026TheorySean Cotner

An example, due to Serre, of a smooth projective surface in positive characteristic whose Picard scheme fails to be reduced, worked out via the two governing dimension inequalities.
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Some examples of algebraic groups

2026TheorySean Cotner

Two pathological phenomena for algebraic groups over general bases — a group degenerating between the multiplicative and additive group across a DVR, and a non-affine identity component — built as centralizers in SL_n.

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