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Intersection Theory and Enumerative Geometry—A Computational Primer (ITEG for short).
In collaboration with Josep M. Miret Biosca and Narcís Sayols Baixeras.

Updated and extended edition of Using Intersection Theory, enriched with the computational environment PyM/WIT (a pure Pythom symbolic system).


Aims of this page

The purpose of this page is to provide free links to the friendly materials (Python files and Jupyter notebooks) produced to endow the subject matter covered in the book with powerful computational companions. The links to the corresponding files have the form py for the Python code and nb for the Jupyter notebook. The functionality is equivalent, as the Python code in the notebooks is taken from that of the corresponding Python file, but deciding which to use in any concrete situation may be a matter of convenience or taste.

The materials are ordered in the same way as the reference to them in the book. They can be downloaded by the user and exploited with the PyM computational system. Since this is work in progress (WiP), please note that the a link remains inert if it is not underlined. To facilitate downloading, links to zip files will be provided in due time for chapters and finally for the whole book. Meanwhile we hope that what is currently available will already be useful, particularly to teachers, students, and researchers of intersection theory and enumerative geometry.

Since the first eight chapters of this book are organized as in Using Intersection Theory, the materials also cover all the computational aspects of that book.

We are grateful, and delighted, to receive feedback from users, particularly if it helps us in improving the whole system.

Index of links

0. Introduction


Chapter 1. Intersecton rings

Chapter 2. Chern Classes

Chapter 3. Projective bundles

Chapter 4. Grassmannians

Chapter 5. Flag varieties

Chapter 6. Concurrent lines

Chapter 7. Characteristic numbers

Chapter 8. Rational equivalence on a blow-up

Chapter 9. Complete quadrics

Chapter 10. Cuspidal plane cubics in P3

Chapter 11. Nodal plane cubics in P3

Chapter 12. Twisted cubics

Chapter 13. Plane curves of degree d with a distinguished multiple point

Chapter 14. Twisted cubics

Chapter 15. Physics-driven enumerative geometry

Chapter 16. Moduli spaces


SXD
2020.01.15