The present volume features contributions from the 2022 BIRS-CMO workshop 'Moduli, Motives and Bundles - New Trends in Algebraic Geometry' held at the Casa Matematica 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.
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ISBN-13
978-1-009-49719-0 (9781009497190)
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Schweitzer Klassifikation
Pedro L. del Angel R. is Professor at the Centro de Investigacion en Matematicas (CIMAT). His research is in algebraic geometry, especially Hodge Theory and algebraic cycles. Frank Neumann is Professor at the University of Pavia. His research is in algebraic topology and algebraic geometry and interactions with number theory and mathematical physics. Alexander H. W. Schmitt is Professor at Freie Universitaet Berlin. He is best-known for his work on moduli spaces of decorated principal bundles. He is the author of 'Geometric Invariant Theory and Decorated Principal Bundles' (2008).
Herausgeber*in
Centro de Investigacion en Matematicas
Universita di Pavia
Freie Universitaet Berlin
Preface; 1. On the stack of 0-dimensional coherent sheaves: structural aspects Barbara Fantechi and Andrea T. Ricolfi; 2. Three lectures on quadratic enumerative geometry Marc Levine; 3. Flat torsors in complex geometry Juan Sebastian Numpaque-Roa and Florent Schaffhauser; 4. Universal chern classes on the moduli of bundles Donu Arapura; 5. Linear stability of coherent systems and applications to Butler's conjecture Abel Castorena, George H. Hitching, and Erick Luna; 6. A Kobayashi-Hitchin correspondence for general coherent systems Cesare Goretti; 7. On the injectivity and non-injectivity of the l-adic cycle class maps Bruno Kahn; 8. A primer on zeta functions and decomposition spaces Andrew Kobin; 9. Atiyah-Bott localization in equivariant Witt cohomology Marc Levine; 10. Base loci, semiampleness, and parallelizable manifolds Ernesto C. Mistretta; 11. Recent developments on compactifications of stacks of shtukas Tuan Ngo Dac and Yakov Varshavsky; 12. A common generalisation of the Andre-Oort and Andre-Pink-Zannier conjectures Rodolphe Richard and Andrei Yafaev.
