Sebastià Xambó-Descamps
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
- WIT user guide
[py |
nb]
- First order and higher order Bernoulli numbers
[py |
nb]
- The Apollonius problem and Lie's circle geometry
[py |
nb]
- Fulton's algorithm for the intersection multiplicity of two plane curves
[py |
nb]
- Kontsevitch's formula for \(N_d\)
[py |
nb]
- Number of \(F_{q^r}\)-rational points on \(F_q\) curves
[py |
nb]
- ITEG practice
[py |
nb]
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