Singularities, Mirror Symmetry, and the Gauged Linear Sigma Model

ISBN-13: 9781470457006

Tyler J. Jarvis;Nathan Priddis

Opis

This volume contains the proceedings of the workshop Crossing the Walls in Enumerative Geometry, held in May 2018 at Snowbird, Utah. It features a collection of both expository and research articles about mirror symmetry, quantized singularity theory (FJRW theory), and the gauged linear sigma model. Most of the expository works are based on introductory lecture series given at the workshop and provide an approachable introduction for graduate students to some fundamental topics in mirror symmetry and singularity theory, including quasimaps, localization, the gauged linear sigma model (GLSM), virtual classes, cosection localization, $p$-fields, and Saito's primitive forms. These articles help readers bridge the gap from the standard graduate curriculum in algebraic geometry to exciting cutting-edge research in the field. The volume also contains several research articles by leading researchers, showcasing new developments in the field.

Spis treści

• R. Webb, Quasimaps and some examples of stacks for everybody
• E. Clader, Introduction to the gauged linear sigma model
• D. Ross, Localization and mirror symmetry
• W.-P. Li, A brief introduction to cosection localization and $P$-fields
• M. Shoemaker, Virtual classes for hypersurfaces via two-periodic complexes
• J. Oh, Localized Chern characters for 2-periodic complexes and virtual cycles
• T. Milanov, Singularity theory and mirror symmetry
• U. Whitcher, Counting points with Berglund-Hubsch-Kravitz mirror symmetry
• H. Fan and Y.-P. Lee, Variations on the theme of quantum Lefschetz
• R. Mi, Type II extremal transitions in Gromov-Witten theory
• C.-C. M. Liu, A lecture on holomorphic anomaly equations and extended holomorphic anomaly equation