The aim of the thesis is the study and the classification of the families of elliptic threefolds which are embedded as anticanonical divisors in some particular P^2-bundle over a surface. In particular, the case where the base surface is the projective plane is studied in depth. The main results of the thesis are: * a theorem on the structure of the non-Kodaira fibres in an elliptic threefold; * the finiteness of the number of families of smooth elliptic threefolds in the P^2-bundle P(L^a + L^b + O) over a surface, where O is the trivial bundle and L is an ample line bundle; * a phisical result concerning F-theory, on the tadpole cancellation and universal tadpole cancellation relations.

ON CALABI-YAU ELLIPTIC THREEFOLDS IN P^2-BUNDLES / A. Cattaneo ; relatore: B. van Geemen ; coordinatore: L. van Geemen. UNIVERSITA' DEGLI STUDI DI MILANO, 2013 Mar 01. 25. ciclo, Anno Accademico 2012. [10.13130/cattaneo-andrea_phd2013-03-01].

ON CALABI-YAU ELLIPTIC THREEFOLDS IN P^2-BUNDLES

A. Cattaneo
2013

Abstract

The aim of the thesis is the study and the classification of the families of elliptic threefolds which are embedded as anticanonical divisors in some particular P^2-bundle over a surface. In particular, the case where the base surface is the projective plane is studied in depth. The main results of the thesis are: * a theorem on the structure of the non-Kodaira fibres in an elliptic threefold; * the finiteness of the number of families of smooth elliptic threefolds in the P^2-bundle P(L^a + L^b + O) over a surface, where O is the trivial bundle and L is an ample line bundle; * a phisical result concerning F-theory, on the tadpole cancellation and universal tadpole cancellation relations.
1-mar-2013
Settore MAT/03 - Geometria
Calabi-Yau ; elliptic fibration ; elliptic threefold
VAN GEEMEN, LAMBERTUS
VAN GEEMEN, LAMBERTUS
Doctoral Thesis
ON CALABI-YAU ELLIPTIC THREEFOLDS IN P^2-BUNDLES / A. Cattaneo ; relatore: B. van Geemen ; coordinatore: L. van Geemen. UNIVERSITA' DEGLI STUDI DI MILANO, 2013 Mar 01. 25. ciclo, Anno Accademico 2012. [10.13130/cattaneo-andrea_phd2013-03-01].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/217720
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