Moduli of Curves
1998
First Published
4.00
Average Rating
382
Number of Pages
Part of Series
A guide to a rich and fascinating algebraic curves and how they vary in families. Providing a broad but compact overview of the field, this book is accessible to readers with a modest background in algebraic geometry. It develops many techniques, including Hilbert schemes, deformation theory, stable reduction, intersection theory, and geometric invariant theory, with the focus on examples and applications arising in the study of moduli of curves. From such foundations, the book goes on to show how moduli spaces of curves are constructed, illustrates typical applications with the proofs of the Brill-Noether and Gieseker-Petri theorems via limit linear series, and surveys the most important results about their geometry ranging from irreducibility and complete subvarieties to ample divisors and Kodaira dimension. With over 180 exercises and 70 figures, the book also provides a concise introduction to the main results and open problems about important topics which are not covered in detail.
Avg Rating
4.00
Number of Ratings
4
5 STARS
50%
4 STARS
25%
3 STARS
0%
2 STARS
25%
1 STARS
0%
goodreads
