Undergraduate Primer in Algebraic Geometry

​Ciro Ciliberto has been a full professor of higher geometry at the University of Roma “Tor Vergata”. Recently, he retired and kept the honorary position of “Docens Turris Virgatae” at the same university. His research fields are algebraic geometry and history of mathematics. He published more than 200 research papers, most of them in top scientific journals, and various books. He spent several research stays abroad, he has been invited to give talks to several international conferences and he is the editor of various scientific journals. Among his hobbies, there are painting and writing.

• 1 Affine and projective algebraic sets.- 2 Basic notions of elimination theory and applications.- 3 Zariski closed subsets and ideals in the polynomials ring.- 4 Some topological properties.- 5 Regular and rational functions.- 6 Morphisms.- 7 Rational maps.- 8 Product of varieties.- 9 More on elimination theory.- 10 Finite morphisms.- 11 Dimension.- 12 The Cayley form.- 13 Grassmannians.- 14 Smooth and singular points.- 15 Power series.- 16 A ne plane curves .- 17 Projective plane curves.- 18 Resolution of singularities of curves.- 19 Divisors, linear equivalence, linear series.- 20 The Riemann-Roch Theorem.

“The text is fairly self-contained … . The clear exposition and numerous exercises also make the text suitable for self-study … . The text is thorough and clearly written, and the numerous exercises do indeed give the reader an algebraic primer to algebraic geometry.” (Kelly Jabbusch, Mathematical Reviews, June, 2022)“New concepts in algebra that one needs, in order to understand the content of the book, are introduced … . I find this feature as an asset of the present book. … the present book is a valuable introduction to algebraic geometry which is nicely written … and a pleasure to read. It can be recommended as a first book for undergraduate courses devoted to algebraic geometry, and also as a supplementary source for standard courses devoted to algebraic geometry.” (Piotr Pokora, zbMATH 1471.14001, 2021)