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Lectures on Gromov–Witten Invariants of Orbifolds

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Enumerative Invariants in Algebraic Geometry and String Theory

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 1947))

This text came out of my CIME minicourse at Cetraro, June 6–11, 2005. I kept the text relatively close to what actually happened in the course. In particular, because of last minutes changes in schedule, the lectures on usual Gromov–Witten theory started after I gave two lectures, so I decided to give a sort of introduction to non-orbifold Gromov–Witten theory, including an exposition of Kontsevich's formula for rational plane curves. From here the gradient of difficulty is relatively high, but I still hope different readers of rather spread-out backgrounds will get something out of it. I gave few computational examples at the end, partly because of lack of time. An additional lecture was given by Jim Bryan on his work on the crepant resolution conjecture with Graber and with Pandharipande, with what I find very exciting computations, and I make some comments on this in the last lecture. In a way, this is the original reason for the existence of orbifold Gromov—Witten theory.

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Authors and Affiliations

  1. Department of Mathematics, Brown University, 1917, Providence, RI 02912, USA

    D. Abramovich

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  1. D. Abramovich
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Editors and Affiliations

  1. Department of Mathematics, University of British Columbia, 1984 Mathematics Rd, Vancouver, V6T 1Z2, BC, Canada

    Kai Behrend

  2. Department of Mathematics “Guido Castelnuovo”, University of Rome “La Sapienza”, P.le Aldo Moro 5, 00185 Rome, Italy

    Marco Manetti

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Abramovich, D. (2008). Lectures on Gromov–Witten Invariants of Orbifolds. In: Behrend, K., Manetti, M. (eds) Enumerative Invariants in Algebraic Geometry and String Theory. Lecture Notes in Mathematics, vol 1947. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79814-9_1

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