A First Course in Algebraic Geometry and Algebraic Varietes

Flaminio Flamini University of Rome “Tor Vergata”, Italy

Endorsement

“The readers are taken by the hand and shown introductory and fundamental notons of Algebraic Geometry. The problems at the end of each chapter are helpful for ensuring a beter understanding and for further practce of the concepts dealt with in the textbook. The clarity of presentaton makes the book suitable and versatle in diferent contexts, not only — as one might assume at frst sight — for the courses of the three-year degree in Mathematcs.”

Gilberto Bini Professor in Geometry University of Palermo, Italy

Descripton

This book provides a gentle introducton to the foundatons of Algebraic Geometry, startng from computatonal topics (ideals and homogeneous ideals, zero loci of ideals) up to increasingly intrinsic and abstract arguments, like “Algebraic Varietes”, whose natural contnuaton is a more advanced course on the theory of schemes, vector bundles and sheaf-cohomology.

aluable to students stud ing lgebraic Geometr and Geometr , A First Course in Algebraic Geometry and Algebraic Varietes contains around 60 solved e ercises to help students thoroughl understand the theories introduced in the book. Proo s o the results are carried out in ull details.

an e amples are discussed which rein orces the understanding o both the theoretcal elements and their conse uences as well as the possible applicatons o the material.

February 2023

Imprint: World Scientfc Publishing Compan Europe

Extent: 300pp

Type: e tbook

Series: Essental e tbooks in athematcs

Main Subject: athematcs

Sub-Subjects: lgebraic Geometr lgebraic opolog

Keywords: ne arietes

Pro ectve arietes lgebraic arietes orphisms o lgebraic arietes atonal and iratonal aps o lgebraic arietes low ups o lgebraic arietes eronese orphisms Segre orphisms lgebraic nvariants o lgebraic arietes

Readership: dvanced undergraduate students (specifcall in their 3rd ear o undergraduate stud or their st ear o postgraduate stud ) in the feld o lgebraic Geometr advanced achelor courses in Geometr or frst courses Geometr during postgraduate stud

Contents

• Pre ace

• asics on Commutatve lgebra

• lgebraic ne Sets

• lgebraic Pro ectve Sets

• opological Propertes. lgebraic arietes

• egular and atonal unctons on lgebraic arietes

• orphisms o lgebraic arietes

• Products o lgebraic arietes

• atonal maps o lgebraic arietes

• Completeness o Pro ectve arietes

• imension o lgebraic arietes

• iber imension. Semicontnuit

• angent Spaces. Smoothness o lgebraic arietes

• Solutons to E ercises

• ibliograph