An Invitation to Modern Enumerative Geometry /
This book is based on a series of lectures given by the author at SISSA, Trieste, within the PhD courses Techniques in enumerative geometry (2019) and Localisation in enumerative geometry (2021). The goal of this book is to provide a gentle introduction, aimed mainly at graduate students, to the fas...
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| Corporate Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
Cham :
Springer International Publishing : Imprint: Springer,
2022.
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| Edition: | 1st ed. 2022. |
| Series: | SISSA Springer Series,
3 |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- 1 Introduction
- 2 Counting in algebraic geometry
- 3 Background material
- 4 Informal introduction to Grassmannians
- 5 Relative Grassmannians, Quot, Hilb
- 6 The Hilbert scheme of points
- 7 Equivariant Cohomology
- 8 The Atiyah-Bott localisation formula
- 9 Applications of the localisation formula
- 10 The toy model for the virtual fundamental class and its localization
- 11 Degree 0 DT invariants of a local Calabi-Yau 3-fold
- 12 DT/PT correspondence and a glimpse of Gromov-Witten theory
- Appendix A: Deformation Theory
- Appendix B: Intersection Theory
- Appendix C: Perfect obstruction theories and virtual classes.