Monads and moduli components for stable rank 2 bundles with odd determinant on the projective space

DOI10.1007/S10711-022-00757-9arXiv2111.13086MaRDI QIDQ6383951

Aislan Leal Fontes, Marcos Jardim

Publication date: 25 November 2021

Abstract: We propose a three-step program for the classification of stable rank 2 bundles on the projective space $mathbb{P}^3$ inspired by an article by Hartshorne and Rao. While this classification program has been successfully completed for stable rank 2 bundles with even determinant and $c_{2}le5$, much less is known for bundles with odd determinant. After revising the known facts about these objects, we list all possible spectra and minimal monads for stable rank 2 bundles with odd determinant and $c_{2}le8$. We provide a full classification of all bundles with positive minimal monads, provide a negative answer to a question raised by Hartshorne and Rao, and describe new irreducible components of the moduli spaces of stable rank 2 bundles with odd determinant and $c_2=6,8$.

Mathematics Subject Classification ID

Vector bundles on surfaces and higher-dimensional varieties, and their moduli (14J60) Algebraic moduli problems, moduli of vector bundles (14D20) Sheaves in algebraic geometry (14F06)

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