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An invitation to quantum cohomology: Kontsevich's formula for rational
plane curves
by Joachim Kock and Israel Vainsencher
xii+159pp., No. 249 of Progress in Mathematics,
Birkhäuser, 2006.

See also http://www.springer.com/birkhauser/mathematics/book/9780817644567
This book is an elementary introduction to stable maps and quantum
cohomology, starting with an introduction to stable pointed curves, and
culminating with a proof of the associativity of the quantum product. The
viewpoint is mostly that of enumerative geometry, and the red thread of the
exposition is the problem of counting rational plane curves. Kontsevich's
formula is initially established in the framework of classical enumerative
geometry, then as a statement about reconstruction for GromovWitten
invariants, and finally, using generating functions, as a special case of
the associativity of the quantum product.
Emphasis is given throughout
the exposition to examples, heuristic discussions, and simple applications
of the basic tools to best convey the intuition behind the subject. The
book demystifies these new quantum techniques by showing how they fit into
classical algebraic geometry.
Some familiarity with basic algebraic geometry and elementary intersection
theory is assumed. Each chapter concludes with some historical comments
and an outline of key topics and themes as a guide for further study,
followed by a collection of exercises that complement the material covered
and reinforce computational skills. As such, the book is ideal for
selfstudy, as a text for a minicourse in quantum cohomology, or as a
special topics text in a standard course in intersection theory. The book
will prove equally useful to graduate students in the classroom setting as
to researchers in geometry and physics who wish to learn about the subject.
Similar books
If you look for this book at flipkart.com, you
will see a list of similar books, among which An Invitation to
Sin by Suzanne Enoch. It has a stockinged leg on the cover.
Unfortunately, from the page of that book, there is no link to
An invitation to quantum cohomology...

ERRATUM: 1.4.3 is a bit misleading, and it is directly wrong to
say "becomes singular" because the variety is already singular.
The paragraph should rather read:
\begin{obs}
Observe that the stabilization of the family $\ov U_{0,4}
\times_{\ov M_{0,4}}\ov U_{0,4} \to \ov U_{0,4}$ is not simply the
blowup along the intersections of the sections as it was the case
for $n=3$. For $n\geq 4$, the projection map has singular fibres,
and it is necesssary also to blow up where the diagonal meets the
singular loci of the fibres (cf.~caseI stabilization). In fact
this blowup results in a smooth variety.
\end{obs}
 In 1.6.5 on page 41, change "had already studied such spaces already in
1968" to "had studied such spaces already in 1968"
 Exercise 9 on p.127: in the list of possibly nonzero 3point
invariants, two are missing, namely
I_{1}(T_{2}T_{4}T_{4})
and
I_{1}(T_{3}T_{4}T_{4}).
(Furthermore, for this reason, in Exercise 10 on p.128, it would be natural to add an
item (iii) asking to compute
I_{1}(T_{2}T_{4}T_{4})
and
I_{1}(T_{3}T_{4}T_{4}).)
(Thanks Howard Nuer).
Last updated: 20120301 by Joachim Kock.