Moduli, Motives and Bundles

New Trends in Algebraic Geometry

Pedro L. del Ángel R., Frank Neumann, Alexander H. W. Schmitt

• Publisher: Cambridge University Press
• Year: 2025
• Topic: Mathematics
• eBook ISBN:
  9781009497213
• Subtopic: Topology
• Index: Mathematics

The present volume features contributions from the 2022 BIRS-CMO workshop 'Moduli, Motives and Bundles – New Trends in Algebraic Geometry' held at the Casa Matemática Oaxaca (CMO), in partnership with the Banff International Research Station for Mathematical Innovation and Discovery (BIRS). The first part presents overview articles on enumerative geometry, moduli stacks of coherent sheaves, and torsors in complex geometry, inspired by related mini course lecture series of the workshop. The second part features invited contributions by experts on a diverse range of recent developments in algebraic geometry, and its interactions with number theory and mathematical physics, offering fresh insights into this active area. Students and young researchers will appreciate this text's accessible approach, as well as its focus on future research directions and open problems.

Table of contents

• Cover
• Series page
• Title page
• Copyright page
• Contents
• List of 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