Beginning in Algebraic Geometry
Introductory textbooks on algebraic geometry typically demand a strong mathematical background and can be challenging even for advanced students. While many excellent texts aim to bridge the gap to mastering this rich field, learners who are new to abstract algebra—or who have never studied it throu...
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| Format: | Online |
| Idioma: | anglès |
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Springer Nature
2025
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| Accés en línia: | ONIX_20250613T105552_9783031888199_15 |
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| _version_ | 1869525341536518144 |
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| author | Clader, Emily Ross, Dustin |
| author_browse | Clader, Emily Ross, Dustin |
| author_facet | Clader, Emily Ross, Dustin |
| author_sort | Clader, Emily |
| collection | Directory of Open Access Books |
| description | Introductory textbooks on algebraic geometry typically demand a strong mathematical background and can be challenging even for advanced students. While many excellent texts aim to bridge the gap to mastering this rich field, learners who are new to abstract algebra—or who have never studied it through a geometric lens—still often find the subject inaccessible. Beginning in Algebraic Geometry achieves a remarkable balance, offering a rigorous and detailed development of algebraic geometry that is nevertheless intended to be readable by students with only a first course in abstract algebra and linear algebra as prerequisites. Starting from the most fundamental properties of polynomials, the reader is guided one step at a time through affine, projective, and quasiprojective algebraic geometry, with complete justifications along the way of such foundational results as the Nullstellensatz and the Theorem on Fiber Dimensions. Several features of this text ensure that it is accessible to the widest possible audience. First, the electronic edition is freely available through Open Access. Furthermore, the authors have skillfully crafted a narrative-driven exposition that reinforces key algebraic concepts (such as quotient rings and modules) and introduces others (such as tensor products and integrality) by developing them within a geometric framework. Well-integrated examples and beautiful illustrations enhance the learning experience, and the writing balances rigor and intuition to maximize readability. Each chapter begins with clearly-stated learning objectives, providing students with a roadmap, and key definitions and results are highlighted for ease of reference. The exercises range from basic to intermediate in difficulty, ensuring sufficient practice without overwhelming the learner. This textbook is suitable for both classroom instruction and independent learners, and it serves as an excellent entry point into the more advanced texts on algebraic geometry. |
| format | Online |
| id | doab-20.500.12854ir-161332 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2025 |
| publishDateRange | 2025 |
| publishDateSort | 2025 |
| publisher | Springer Nature |
| publisherStr | Springer Nature |
| record_format | ojs |
| spelling | doab-20.500.12854ir-1613322025-06-14T05:02:57Z Beginning in Algebraic Geometry Clader, Emily Ross, Dustin undergrad algebraic geometry textbook algebraic geometry textbook polynomial rings affine algebraic geometry varieties and ideals coordinate rings polynomial maps Nullstellensatz projective algebraic geometry quasiprojective varieties thema EDItEUR::P Mathematics and Science::PB Mathematics::PBM Geometry::PBMW Algebraic geometry Introductory textbooks on algebraic geometry typically demand a strong mathematical background and can be challenging even for advanced students. While many excellent texts aim to bridge the gap to mastering this rich field, learners who are new to abstract algebra—or who have never studied it through a geometric lens—still often find the subject inaccessible. Beginning in Algebraic Geometry achieves a remarkable balance, offering a rigorous and detailed development of algebraic geometry that is nevertheless intended to be readable by students with only a first course in abstract algebra and linear algebra as prerequisites. Starting from the most fundamental properties of polynomials, the reader is guided one step at a time through affine, projective, and quasiprojective algebraic geometry, with complete justifications along the way of such foundational results as the Nullstellensatz and the Theorem on Fiber Dimensions. Several features of this text ensure that it is accessible to the widest possible audience. First, the electronic edition is freely available through Open Access. Furthermore, the authors have skillfully crafted a narrative-driven exposition that reinforces key algebraic concepts (such as quotient rings and modules) and introduces others (such as tensor products and integrality) by developing them within a geometric framework. Well-integrated examples and beautiful illustrations enhance the learning experience, and the writing balances rigor and intuition to maximize readability. Each chapter begins with clearly-stated learning objectives, providing students with a roadmap, and key definitions and results are highlighted for ease of reference. The exercises range from basic to intermediate in difficulty, ensuring sufficient practice without overwhelming the learner. This textbook is suitable for both classroom instruction and independent learners, and it serves as an excellent entry point into the more advanced texts on algebraic geometry. 2025-06-14T05:02:56Z 2025-06-14T05:02:56Z 2025-06-13T09:19:51Z 2025 book ONIX_20250613T105552_9783031888199_15 https://library.oapen.org/handle/20.500.12657/103560 9783031888199 9783031888182 https://directory.doabooks.org/handle/20.500.12854/161332 eng Undergraduate Texts in Mathematics open access image/jpeg n/a https://library.oapen.org/bitstream/20.500.12657/103560/1/9783031888199.pdf Springer Nature Springer Nature Switzerland 10.1007/978-3-031-88819-9 10.1007/978-3-031-88819-9 9fa3421d-f917-4153-b9ab-fc337c396b5a 9783031888199 9783031888182 Springer Nature Switzerland 421 Cham open access |
| spellingShingle | undergrad algebraic geometry textbook algebraic geometry textbook polynomial rings affine algebraic geometry varieties and ideals coordinate rings polynomial maps Nullstellensatz projective algebraic geometry quasiprojective varieties thema EDItEUR::P Mathematics and Science::PB Mathematics::PBM Geometry::PBMW Algebraic geometry Clader, Emily Ross, Dustin Beginning in Algebraic Geometry |
| title | Beginning in Algebraic Geometry |
| title_full | Beginning in Algebraic Geometry |
| title_fullStr | Beginning in Algebraic Geometry |
| title_full_unstemmed | Beginning in Algebraic Geometry |
| title_short | Beginning in Algebraic Geometry |
| title_sort | beginning in algebraic geometry |
| topic | undergrad algebraic geometry textbook algebraic geometry textbook polynomial rings affine algebraic geometry varieties and ideals coordinate rings polynomial maps Nullstellensatz projective algebraic geometry quasiprojective varieties thema EDItEUR::P Mathematics and Science::PB Mathematics::PBM Geometry::PBMW Algebraic geometry |
| topic_facet | undergrad algebraic geometry textbook algebraic geometry textbook polynomial rings affine algebraic geometry varieties and ideals coordinate rings polynomial maps Nullstellensatz projective algebraic geometry quasiprojective varieties thema EDItEUR::P Mathematics and Science::PB Mathematics::PBM Geometry::PBMW Algebraic geometry |
| url | ONIX_20250613T105552_9783031888199_15 |
| work_keys_str_mv | AT claderemily beginninginalgebraicgeometry AT rossdustin beginninginalgebraicgeometry |