# The Moduli Space of Curves

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Part of the Progress in Mathematics book series (PM, volume 129)

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- 304 Citations
- 18k Downloads

Part of the Progress in Mathematics book series (PM, volume 129)

The moduli space *M _{g} *of curves of fixed genus

Leading experts in the field explore in this volume both the structure of the moduli space of curves and its relationship with physics through quantum cohomology. Altogether, this is a lively volume that testifies to the ferment in the field and gives an excellent view of the state of the art for both mathematicians and theoretical physicists. It is a persuasive example of the famous Wignes comment, and its converse, on "the unreasonable effectiveness of mathematics in the natural science."

Witteen’s conjecture in 1990 describing the intersection behavior of tautological classes in the cohomology of *M _{g}* arose directly from string theory. Shortly thereafter a stunning proof was provided by Kontsevich who, in this volume, describes his solution to the problem of counting rational curves on certain algebraic varieties and includes numerous suggestions for further development. The same problem is given an elegant treatment in a paper by Manin. There follows a number of contributions to the geometry, cohomology, and arithmetic of the moduli spaces of curves. In addition, several contributors address quantum cohomology and conformal field theory.

Arithmetic Cohomology Counting algebra algebraic geometry algebraic varieties function geometry mathematics moduli space proof theoretical physics

- DOI https://doi.org/10.1007/978-1-4612-4264-2
- Copyright Information Birkhäuser Boston 1995
- Publisher Name Birkhäuser Boston
- eBook Packages Springer Book Archive
- Print ISBN 978-1-4612-8714-8
- Online ISBN 978-1-4612-4264-2
- Series Print ISSN 0743-1643
- Series Online ISSN 2296-505X
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