Topics in The Geometry of Projective Space Recent Work of fl Zak

The main topics discussed at the D. M. V. Seminar were the connectedness theorems of Fulton and Hansen, linear normality and subvarieties of small codimension in projective spaces. They are closely related; thus the connectedness theorem can be used to prove the inequality-part of Hartshorne's conjecture on linear normality, whereas Deligne's generalisation of the connectedness theorem leads to a refinement of Barth's results on the topology of varieties with small codimension in a projective space. The material concerning the connectedness theorem itself (including the highly surprising application to tamely ramified coverings of the projective plane) can be found in the paper by Fulton and the first author: W. Fulton, R. Lazarsfeld, Connectivity and its applications in algebraic geometry, Lecture Notes in Math. 862, p. 26-92 (Springer 1981).

Fascinating and surprising developments are taking place in the classification of algebraic varieties. The work of Hacon and McKernan and many others is causing a wave of breakthroughs in the minimal model program: we now know that for a smooth projective variety the canonical ring is finitely generated.

Algebra & Geometry: An Introduction to University Mathematics, Second Edition provides a bridge between high school and undergraduate mathematics courses on algebra and geometry.

This book presents very recent results involving an extensive use of analytical tools in the study of geometrical and topological properties of complete Riemannian manifolds. It analyzes in detail an extension of the Bochner technique to the non compact setting, yielding conditions which ensure that solutions of geometrically significant differential equations either are trivial (vanishing results) or give rise to finite dimensional vector spaces (finiteness results). The book develops a range of methods from spectral theory and qualitative properties of solutions of PDEs to comparison theorems in Riemannian geometry and potential theory.

This book presents very recent results involving an extensive use of analytical tools in the study of geometrical and topological properties of complete Riemannian manifolds. It analyzes in detail an extension of the Bochner technique to the non compact setting, yielding conditions which ensure that solutions of geometrically significant differential equations either are trivial (vanishing results) or give rise to finite dimensional vector spaces (finiteness results). The book develops a range of methods from spectral theory and qualitative properties of solutions of PDEs to comparison theorems in Riemannian geometry and potential theory.

This book covers the most important topics in the field of personalized orthopedics. It starts with the 3D geometry of the bones, focusing on the problem of reverse engineering of the bones. It also shows the application of a 3D geometric model of bone for the design of personalized implants and prostheses.

This book covers the most important topics in the field of personalized orthopedics. It starts with the 3D geometry of the bones, focusing on the problem of reverse engineering of the bones. It also shows the application of a 3D geometric model of bone for the design of personalized implants and prostheses.