Book contents
- Frontmatter
- Contents
- Contributors
- Preface
- 1 On the Stack of 0-Dimensional Coherent Sheaves: Structural Aspects
- 2 Three Lectures on Quadratic Enumerative Geometry
- 3 Flat Torsors in Complex Geometry
- 4 Universal Chern Classes on the Moduli of Bundles
- 5 Linear Stability of Coherent Systems and Applications to Butler’s Conjecture
- 6 A Kobayashi–Hitchin Correspondence for General Coherent Systems
- 7 On the Injectivity and Non-injectivity of the l-Adic Cycle Class Maps
- 8 A Primer on Zeta Functions and Decomposition Spaces
- 9 Atiyah–Bott Localization in Equivariant Witt Cohomology
- 10 Base Loci, Semiampleness, and Parallelizable Manifolds
- 11 Recent Developments on Compactifications of Stacks of Shtukas
- 12 A Common Generalisation of the André–Oort and André–Pink–Zannier Conjectures
- References
3 - Flat Torsors in Complex Geometry
Published online by Cambridge University Press: 31 October 2025
Book contents
- Frontmatter
- Contents
- Contributors
- Preface
- 1 On the Stack of 0-Dimensional Coherent Sheaves: Structural Aspects
- 2 Three Lectures on Quadratic Enumerative Geometry
- 3 Flat Torsors in Complex Geometry
- 4 Universal Chern Classes on the Moduli of Bundles
- 5 Linear Stability of Coherent Systems and Applications to Butler’s Conjecture
- 6 A Kobayashi–Hitchin Correspondence for General Coherent Systems
- 7 On the Injectivity and Non-injectivity of the l-Adic Cycle Class Maps
- 8 A Primer on Zeta Functions and Decomposition Spaces
- 9 Atiyah–Bott Localization in Equivariant Witt Cohomology
- 10 Base Loci, Semiampleness, and Parallelizable Manifolds
- 11 Recent Developments on Compactifications of Stacks of Shtukas
- 12 A Common Generalisation of the André–Oort and André–Pink–Zannier Conjectures
- References
Summary
These notes grew out of a mini-course given by the second-named author at Casa Matemática Oaxaca in the Fall of 2022. Their purpose is to provide an exposition, directed at graduate students, of the basic properties of complex analytic group bundles and torsors under them, including the flat case.
Information
- Type
- Chapter
- Information
- Moduli, Motives and BundlesNew Trends in Algebraic Geometry, pp. 106 - 142Publisher: Cambridge University PressPrint publication year: 2025
References
Atiyah, M. F.. Complex analytic connections in fibre bundles. Trans. Am. Math. Soc., 85:181–207, 1957.10.1090/S0002-9947-1957-0086359-5CrossRefGoogle Scholar
Grauert, H.. Généralisation d’un théorème de Runge et application à la théorie des espaces fibrés analytiques. C. R. Acad. Sci. Paris, 242:603–605, 1956.Google Scholar
Grothendieck, A.. A General Theory of Fibre Spaces with Structure Sheaf. University of Kansas, Report No. 4, 1955. https://agrothendieck.github.io/divers/kansasscan.pdf.Google Scholar
Grothendieck, A.. Sur le mémoire de Weil. Généralisation des fonctions abéliennes. In Séminaire Bourbaki : années 1956/57–1957/58, exposés 137-168, number 4 in Séminaire Bourbaki, pages 57–71. Société mathématique de France, 1958. talk:141.Google Scholar
Seshadri, C. S.. Remarks on parabolic structures. In Vector bundles and complex geometry. Conference on vector bundles in honor of S. Ramanan on the occasion of his 70th birthday, Madrid, Spain, June 16–20, 2008., pages 171–182. Providence, RI: American Mathematical Society (AMS), 2010.Google Scholar
Steenrod, N.. The topology of fibre bundles. Princeton, NJ: Princeton University Press, 1951.10.1515/9781400883875CrossRefGoogle Scholar
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