Configuration of points and strings

Abstract

Let $X$ be a smooth projective variety of dimension $n\ge 2$. It is shown that a finite configuration of points on $X$ subject to certain geometric conditions possesses rich inner structure. On the mathematical level this inner structure is a variation of Hodge-like structure. As a consequence one can attach to such point configurations: (i) Lie algebras and their representations (ii) Fano toric variety whose hyperplane sections are Calabi-Yau varieties. These features lead to a picture which is very suggestive of quantum gravity according to string theory.

32 pages, 1 figure this version will appear in Journal of Geometry and Physics

References in corpus (1)

• Reconstruction of a variety from the derived category and groups of autoequivalences

Cited by in corpus (1)

• Seminatural bundles of rank two, degree one and $c_2=10$ on a quintic surface