an:01115545
Zbl 0918.14011
Kaufmann, Ralph M.
The geometry of moduli spaces of pointed curves, the tensor product in the theory of Frobenius manifolds and the explicit K??nneth formula in quantum cohomology
EN
Bonner Mathematische Schriften. 312. Bonn: Univ. Bonn, Mathematisch-Naturwissenschaftliche Fakult??t, 95 p. (1998).
00430399
1998
b
14H10 14F99 55N20 81T30
moduli space of pointed curves of genus 0; Weil-Petersson volumes; K??nneth formula for quantum cohomology; Calabi-Yau manifolds
This thesis develops further the results of an article by \textit{R. Kaufmann}, \textit{Yu. Manin} and \textit{D. Zagier} [Commun. Math. Phys. 181, No. 3, 763-787 (1996; Zbl 0890.14011)] and their applications.
It has three chapters. The first one discusses the intersection of strata classes in \(\overline M_{g,n}\) and provides the formulae for the intersection matrices in cohomology of \(\overline{M_{0,n}}\) (moduli space of pointed curves of genus 0), and for Weil-Petersson volumes. These results are used in chapter two to define the tensor product of the pointed Frobenius manifolds. In chapter 3 the formulae from chapters 1 and 2 are used to derive the explicit K??nneth formula for quantum cohomology. Examples of products of two and three 3-dimensional Calabi-Yau manifolds are discussed at the end.
A.Rudakov (Trondheim)
Zbl 0890.14011