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Graded Algebras in Algebraic Geometry

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The objective of this book is to look at certain commutative graded algebras that appear frequently in algebraic geometry. By studying classical constructions from geometry from the point of view of modern commutative algebra, this carefully-written book is a valuable source of information, offering a careful algebraic systematization and treatment of the problems at hand, and contributing to the study of the original geometric questions. In greater detail, the material covers aspects of rational maps (graph, degree, birationality, specialization, combinatorics), Cremona transformations, polar maps, Gauss maps, the geometry of Fitting ideals, tangent varieties, joins and secants, Aluffi algebras. The book includes sections of exercises to help put in practice the theoretic material instead of the mere complementary additions to the theory.

Author(s): Aron Simis, Zaqueu Ramos
Series: De Gruyter Expositions in Mathematics, 70
Publisher: De Gruyter
Year: 2022

Language: English
Pages: 463
City: Berlin

Acknowledgments
Foreword
Contents
1 Geometric motivation
2 Graded algebras
3 Rational maps, I
4 Rational maps, II
5 The gradient ideal
6 Cremona transformations, I
7 Cremona transformations, II
8 Steps in elimination
9 The Gauss map
10 Tangent varieties
11 Embedded joins and secants
12 Aluffi algebras
Bibliography
Index