Mathematics – Commutative Algebra
Scientific paper
2009-05-17
Mathematics
Commutative Algebra
24/25 pages (A4/letter); Revisions: v1 - as submitted for publication. Contains the actual Macaulay2-code and explanation as
Scientific paper
Motivated 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 $\pi \colon Z \to X$, where $Z$ is the total space of a negative bundle over $\mathbb{P}^1$ and $\pi$ contracts the zero section. We obtain two numerical invariants of a rank-2 vector bundle $E$ on $Z$, the width $h^0\bigl(X; (\pi_*E)^{\vee \vee} \bigl/ \pi_*E\bigr)$ and the height $h^0\bigl(X; R^1 \pi_*E \bigr)$, whose sum is the local holomorphic Euler characteristic $\chi^\text{loc}(E)$.
Köppe Thomas
No associations
LandOfFree
Computations of instanton invariants does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Computations of instanton invariants, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Computations of instanton invariants will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-514640