Computations of instanton invariants

dc.creatorKöppe, Thomas
dc.date2009-05-17
dc.date.accessioned2026-07-07T13:15:56Z
dc.date.available2026-07-07T13:15:56Z
dc.descriptionMotivated by newly discovered properties of instantons on non-compact spaces, we realised that certain analytic invariants of vector bundles detect fine geometric properties. We present numerical algorithms, implemented in Macaulay 2, to compute these invariants. Precisely, we obtain the direct image and first derived functor of the contraction map $π\colon Z \to X$, where $Z$ is the total space of a negative bundle over $\mathbb{P}^1$ and $π$ contracts the zero section. We obtain two numerical invariants of a rank-2 vector bundle $E$ on $Z$, the width $h^0\bigl(X; (π_*E)^{\vee \vee} \bigl/ π_*E\bigr)$ and the height $h^0\bigl(X; R^1 π_*E \bigr)$, whose sum is the local holomorphic Euler characteristic $χ^\text{loc}(E)$.
dc.description24/25 pages (A4/letter); Revisions: v1 - as submitted for publication. Contains the actual Macaulay2-code and explanation as attachments
dc.identifierhttps://arxiv.org/abs/0905.2745
dc.identifierhttp://arxiv.org/abs/0905.2745
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/230634
dc.subjectCommutative Algebra
dc.subject14Q99; 12Y05; 68W30
dc.titleComputations of instanton invariants
dc.typetext

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