Explore nonrational toric geometry through a lecture that establishes a correspondence between simplicial fans and foliated complex manifolds called LVMB manifolds. Delve into toric quasifolds as leaf spaces, examining how the interplay between toric geometry and combinatorics extends to nonrational contexts. Investigate a one-parameter family of toric quasifolds containing Hirzebruch surfaces from a foliation perspective. Learn about Stanley's g-Theorem proof reformulation for simple polytope combinatorics and discover the rich connections between convex geometry, Gale duality, and holomorphic foliations in this advanced mathematical exploration.
Nonrational Toric Geometry III - Quasifolds, Foliations, Combinatorics and One-parameter Families
Overview
Syllabus
Intro
INTRODUCTION: PREVIOUS TALKS
INTRODUCTION: REMARKS
INTRODUCTION MOTIVATIONS
INTRODUCTION: A NEW FRAMEWORK, B.-ZAFFRAN (2015)
HOLOMORPHIC PRINCIPAL BUNDLES OVER PROJECTIVE TORIC VARIETIES L. MERRSEMAN, A. VERJOVSKY (2004)
NONRATIONAL TORIC GEOMETRY IN THE FRAMEWORK OF POLIATIONS (B.-ZAFFRAN): CONVEX GEOMETRIC SIDE
CONVEX GEOMETRIC SIDE: TRIANGULATED VECTOR
WHY TRIANGULATED VECTOR CONFIGURATIONS? CONVEX GEOMETRIC DATA POR LVMB MANIFOLDS
CONVEX GEOMETRIC DATA FOR LVMB MANIFOLDS
GALE DUALITY
CONSTRUCTION OF LVMB MANIFOLDS
THE HOLOMORPHIC FOLIATION
RATIONALITY MEASURE OF V AND LEAVES TOPOLOGICAL TYE
FOLIATIONS MODELING COMPLEX TORIC QUASIFOLDS
MODEL EXAMPLES: THE FAN OF CP
THE HIRZEBRUCH FAMILY, B-PRATO-ZAFFRAN 2019
BASIC COHOMOLOGY, AGAIN B-ZAFFRAN (2015)
COMPUTATION OF BASIC BETTI NUMBERS
STANLEY'S THEOREM RIVISITED
STANLEY'S ARGUMENT ADAPTED
RELATED WORKS AND PERSPECTIVES
BIBLIOGRAPHY OF THE MINICOURSE
Taught by
IMSA
