Ce. volume. u.t fioJtme de. la Ve.M-ion de6~ve. du .te.x.tu du cOn6Vte.n.cV6 fia-i.tu a N-ice. au cowu., d' un CoUoque. qu-i f.>' Ij u.t .te.n.u du 23 au 27 Ju-in 1981. Comme. Ie. f.>ugge.ILe. Mn ~e., Ie. f.>uje..t, volon..t~e.me.n..t ILU.tfLe.-in..t, gfLav-i.ta-i.t gILof.>f.>o-modo au.toulL du upacu pILoje.c.t-i6f.> de. pe..t-i.te. d-ime.n­ f.>-ion e..t du co UfLbe.f.> , ce.la f.>UfL un COfLpf.> aigebfL-ique.me.n..t elM. Ii f.>e.mble. que. ce. cho-ix deUbVte a-i.t Ue b-ie.n accu~ danf.> I' e.nf.>e.mble. pM lu pa.Jt:ttupan..tf.>. Le. Colloque. a IL(LMe.mble une. M-ixan..ta-in.e. de. f.>peu~.tu ve.n.uf.> de. d-i66eILe.n..tf.> paljf.> e..t nouf.> noUf.> f.>ommu e.n pa.Jt:ttcuUe.fL ILejo~ de. l'-im­ pofL.tan..te. pa.Jt:ttc-ipatio n de. nof.> vo~-inf.> -i.taUe.nf.>. Le. pIL06Uf.>e.UfL VIEuVONNE n'aljaYt.t paf.> pu pa.Jt:ttupe.fL au colloque.

Perhaps the most famous example of how ideas from modern physics have revolutionized mathematics is the way string theory has led to an overhaul of enumerative geometry, an area of mathematics that started in the eighteen hundreds. Century-old problems of enumerating geometric configurations have now been solved using new and deep mathematical techniques inspired by physics! The book begins with an insightful introduction to enumerative geometry. From there, the goal becomes explaining the more advanced elements of enumerative algebraic geometry. Along the way, there are some crash courses on intermediate topics which are essential tools for the student of modern mathematics, such as cohomology and other topics in geometry. The physics content assumes nothing beyond a first undergraduate course. The focus is on explaining the action principle in physics, the idea of string theory, and how these directly lead to questions in geometry. Once these topics are in place, the connection between physics and enumerative geometry is made with the introduction of topological quantum field theory and quantum cohomology.

Algebraic geometry has benefited enormously from the powerful general machinery developed in the latter half of the twentieth century. The cost has been that much of the research of previous generations is in a language unintelligible to modern workers, in particular, the rich legacy of classical algebraic geometry, such as plane algebraic curves of low degree, special algebraic surfaces, theta functions, Cremona transformations, the theory of apolarity and the geometry of lines in projective spaces. The author's contemporary approach makes this legacy accessible to modern algebraic geometers and to others who are interested in applying classical results. The vast bibliography of over 600 references is complemented by an array of exercises that extend or exemplify results given in the book.

Ce. volume. u.t fioJtme de. la Ve. M-ion de6~ve. du .te.x.tu du cOn6Vte.n.cV6 fia-i.tu a N-ice. au cowu., d' un CoUoque. qu-i f.>' Ij u.t .te.n.u du 23 au 27 Ju-in 1981. Comme. Ie. f.>ugge. ILe. Mn ~e., Ie. f.>uje.t, volon.t~e.me.n.t ILU.tfLe.-in.t, gfLav-i.ta-i.t gILof.>f.>o-modo au.toulL du upacu pILoje.c.t-i6f.> de. pe.t-i.te. d-ime.n f.>-ion e.t du co UfLbe.f.>, ce.la f.>UfL un COfLpf.> aigebfL-ique.me.n.t elM. Ii f.>e.mble. que. ce. cho-ix deUbVte a-i.t Ue b-ie.n accu~ danf.> I' e.nf.>e.mble. pM lu pa. Jt:ttupan.tf.>. Le. Colloque. a IL(LMe.mble une. M-ixan.ta-in.e. de. f.>peu~.tu ve.n.uf.> de. d-i66eILe.n.tf.> paljf.> e.t nouf.> noUf.> f.>ommu e.n pa. Jt:ttcuUe.fL ILejo~ de. l'-im pofL.tan.te. pa. Jt:ttc-ipatio n de. nof.> vo~-inf.> -i.taUe.nf.>. Le. pIL06Uf.>e. UfL VIEuVONNE n'aljaYt.t paf.> pu pa. Jt:ttupe.fL au colloque.

3264, the mathematical solution to a question concerning geometric figures.