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Main Authors:	Coskun, Izzet, Ross, Julius
Format:	Preprint
Published:	2025
Subjects:	Algebraic Geometry 14C25
Online Access:	https://arxiv.org/abs/2509.03747
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author	Coskun, Izzet Ross, Julius
author_facet	Coskun, Izzet Ross, Julius
contents	The study of irreducible subvarieties has recently seen a surge of interest due to connections with convex geometry. In this paper, we study cohomology classes of Grassmannians that are realizable by irreducible subvarieties. We completely classify the cohomology classes that can be realized by irreducible subvarieties in dimensions 2 and 3 and codimensions 2 and 3. We also classify all the classes that can be realizable by an irreducible subvariety for the Grassmannians $G(2,n)$ for $n \leq 6$ and $G(3,6)$. We classify the cohomology classes in all dimensions that are, up to positive multiple, realizable by an irreducible subvariety for the Grassmannians $G(2,n)$.
format	Preprint
id	arxiv_https___arxiv_org_abs_2509_03747
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	Realization of Cohomology Classes in Grassmannians Coskun, Izzet Ross, Julius Algebraic Geometry 14C25 The study of irreducible subvarieties has recently seen a surge of interest due to connections with convex geometry. In this paper, we study cohomology classes of Grassmannians that are realizable by irreducible subvarieties. We completely classify the cohomology classes that can be realized by irreducible subvarieties in dimensions 2 and 3 and codimensions 2 and 3. We also classify all the classes that can be realizable by an irreducible subvariety for the Grassmannians $G(2,n)$ for $n \leq 6$ and $G(3,6)$. We classify the cohomology classes in all dimensions that are, up to positive multiple, realizable by an irreducible subvariety for the Grassmannians $G(2,n)$.
title	Realization of Cohomology Classes in Grassmannians
topic	Algebraic Geometry 14C25
url	https://arxiv.org/abs/2509.03747

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