Details
| Originalsprache | Englisch |
|---|---|
| Aufsatznummer | 103597 |
| Fachzeitschrift | Journal of geometry and physics |
| Jahrgang | 150 |
| Frühes Online-Datum | 17 Jan. 2020 |
| Publikationsstatus | Veröffentlicht - Apr. 2020 |
| Extern publiziert | Ja |
Abstract
Given a vector bundle E on a smooth projective curve or surface X carrying the structure of a V-twisted Hitchin pair for some vector bundle V, we observe that the associated tautological bundle E[n] on the punctual Hilbert scheme of points X[n] has an induced structure of a ((V∨)[n])∨-twisted Hitchin pair, where (V∨)[n] is a vector bundle on X[n] constructed using the dual V∨ of V. In particular, a Higgs bundle on X induces a logarithmic Higgs bundle on the Hilbert scheme X[n]. We then show that the known results on stability of tautological bundles and reconstruction from tautological bundles generalize to tautological Hitchin pairs.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Mathematische Physik
- Physik und Astronomie (insg.)
- Mathematik (insg.)
- Geometrie und Topologie
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in: Journal of geometry and physics, Jahrgang 150, 103597, 04.2020.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Fourier–Mukai transformation and logarithmic Higgs bundles on punctual Hilbert schemes
AU - Biswas, Indranil
AU - Krug, Andreas
PY - 2020/4
Y1 - 2020/4
N2 - Given a vector bundle E on a smooth projective curve or surface X carrying the structure of a V-twisted Hitchin pair for some vector bundle V, we observe that the associated tautological bundle E[n] on the punctual Hilbert scheme of points X[n] has an induced structure of a ((V∨)[n])∨-twisted Hitchin pair, where (V∨)[n] is a vector bundle on X[n] constructed using the dual V∨ of V. In particular, a Higgs bundle on X induces a logarithmic Higgs bundle on the Hilbert scheme X[n]. We then show that the known results on stability of tautological bundles and reconstruction from tautological bundles generalize to tautological Hitchin pairs.
AB - Given a vector bundle E on a smooth projective curve or surface X carrying the structure of a V-twisted Hitchin pair for some vector bundle V, we observe that the associated tautological bundle E[n] on the punctual Hilbert scheme of points X[n] has an induced structure of a ((V∨)[n])∨-twisted Hitchin pair, where (V∨)[n] is a vector bundle on X[n] constructed using the dual V∨ of V. In particular, a Higgs bundle on X induces a logarithmic Higgs bundle on the Hilbert scheme X[n]. We then show that the known results on stability of tautological bundles and reconstruction from tautological bundles generalize to tautological Hitchin pairs.
KW - Fourier–Mukai transformation
KW - Hilbert scheme
KW - Logarithmic Higgs bundle
KW - Stability
UR - http://www.scopus.com/inward/record.url?scp=85078086821&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1903.01641
DO - 10.48550/arXiv.1903.01641
M3 - Article
AN - SCOPUS:85078086821
VL - 150
JO - Journal of geometry and physics
JF - Journal of geometry and physics
SN - 0393-0440
M1 - 103597
ER -