Algebraic Geometries - An Introduction

Pasquale De Marco

Summary

**Algebraic Geometries: An Introduction** is a comprehensive and accessible introduction to algebraic geometry, a vast and active field of mathematics with applications to many other areas of mathematics, including number theory, topology, and differential geometry.Written for undergraduate and graduate students with a background in abstract algebra and linear algebra, this book covers the basic concepts of algebraic geometry, including algebraic varieties, regular functions, differential forms, sheaves, and cohomology. It also includes some more advanced topics, such as moduli spaces, arithmetic geometry, and algebraic geometry and physics.One of the main themes of algebraic geometry is the study of moduli spaces. A moduli space is a space whose points represent algebraic varieties of a given type. For example, the moduli space of elliptic curves is a space whose points represent all elliptic curves. Moduli spaces are important because they provide a way to understand the structure of algebraic varieties.Another important theme of algebraic geometry is the study of arithmetic geometry. Arithmetic geometry is the study of the relationship between algebraic geometry and number theory. For example, one can use algebraic geometry to study Diophantine equations, which are equations whose solutions are integers. Arithmetic geometry is a very active area of research, and it has led to many important results in number theory.Finally, algebraic geometry has many applications to physics. For example, algebraic geometry is used in string theory, mirror symmetry, and quantum cohomology. Algebraic geometry is also used in topological field theories, which are mathematical models of physical phenomena.**Algebraic Geometries: An Introduction** is written in a clear and concise style, and it includes many examples and exercises to help the reader understand the material. It is an ideal textbook for a one-semester or two-semester course in algebraic geometry, and it is also a valuable resource for researchers in other areas of mathematics and physics.If you like this book, write a review!

Available since: 06/02/2025.

Print length: 152 pages.

Science & Technology

Other books that might interest you

Data Science with Python for...

Brian Paul

In this accessible and engaging book, you'll traverse the fundamentals of Python programming, seamlessly transitioning into the realm of data science. From setting up your Python environment to mastering essential libraries like NumPy, Pandas, and Matplotlib, each chapter builds upon the last, providing a scaffolded approach to learning.
Explore the art of data wrangling with Pandas, gaining proficiency in cleaning, preprocessing, and merging datasets. Demystify the complexities of exploratory data analysis (EDA) and statistical concepts, empowering you to make informed decisions and draw valuable insights from your data.
Dive into the heart of machine learning, where you'll grasp the basics of model training, evaluation, and hyperparameter tuning using the powerful Scikit-Learn library. Discover the significance of feature engineering, delve into time series analysis, and unravel the potential of big data with Apache Spark and Dask.
As you progress, the book navigates through advanced tools for data visualization, such as Plotly and Dash, allowing you to create stunning and interactive visualizations that bring your data to life. Uncover the ethical considerations in data science, addressing bias, privacy, and security, and cap off your journey with real-world projects and case studies, cementing your newfound skills.
"Data Science with Python for Beginners" is not just a book; it's your companion in the evolving landscape of data science. Packed with practical examples, exercises, and hands-on projects, this guide instills confidence in beginners and ignites a passion for data exploration and analysis. Whether you aspire to make data-driven decisions or embark on a career in data science, this book is your key to unlocking the doors of insight and innovation. Let Python be your guide as you unravel the vast possibilities of data science!

Show book

The Planet You Inherit - Letters...

Larry L. Rasmussen

For the first time ever, love letters consciously written by elders of one geologic epoch to the young of another. 
 
 
 
Our children's and grandchildren's generation will face a different world, one affected by climate instability, mass uncertainty, and breathtaking extinction. In fact, the next generation will face the reality that human activity is changing the planet from one geological epoch to another. 
 
 
 
From this vantage point—two generations across two geological epochs facing a fundamentally changing planet—Larry Rasmussen writes to his grandchildren. As a grandfather invested in a green earth and climate justice as well as a scholar of faith-based earth ethics, Rasmussen bridges this gap between generations to write to the future about climate change, global citizenship, democracy, and legacy. In topics ranging from "A Viable Way of Life" and "Democracy" to "Where We've Come From" and "Who We Are Now," Rasmussen explores the large questions of justice, meaning, and faith, encouraging us to speak to and look to the future generation and their future world.

Show book

The AI Factor - How to Apply...

Asha Saxena, Seth Dobrin

Have you heard about artificial intelligence (AI) and big data but felt they are technologies too big or too complicated for you or your business? Do you imagine AI as a Hollywood science fiction stereotype or something in the far and distant future? 
 
 
 
Take heart. AI is none of those things. It's part of our everyday lives, and it has the power to transform your business. 
 
 
 
This book will put AI, big data, the cloud, robotics, and smart devices in context. It will reveal how these technologies can dramatically multiply any businesses—including yours—by strategically using your data's latent, transformative potential. 
 
 
 
Noted business leader, data consultant, and Columbia professor Asha Saxena has distilled her twenty-seven years of experience teaching Fortune 500 leaders in this powerful and insightful book. In The AI Factor, business leaders will learn how to understand the data they already have and how to use it innovatively to grow their businesses using Saxena's unique methodology.

Show book

Hypnosis for weight loss...

Stuart Newman

Hypnosis for weight loss with DST Hypno and Stu Newman is an effective way to create a subconscious motivation to eat healthily.  
Through hypnotherapy, you can re-program your mind so that you are more likely to make healthier food choices.  
This process helps you break free from unhealthy habits, such as binge eating or emotional eating.  
With the help of Stu Newman’s experienced guidance, he will guide your mind into a relaxed state in order for positive suggestions about healthy living and nutrition to be accepted by your subconscious mind.  
In addition, this type of therapy also enables you to identify any underlying issues which may have been causing cravings for unhealthy foods in the first place; thus allowing them to be addressed and resolved effectively over time.  
So if you're looking for an effective way of creating lasting change when it comes achieving long term weight loss goals then hypnosis is certainly worth considering!

Show book

A Croft in the Hills

Katharine Stewart, Neil Gunn

A Croft in the Hills captures, in simple, moving descriptions, what it was really like trying to make a living out of a hill croft near Loch Ness fifty years ago. A couple and their young daughter, fresh from city life, immerse themselves in the practicalities of looking after sheep, cattle and hens, mending fences, baking bread, and surviving the worst that Scottish winters can throw at them. 
 
 
 
Their neighbors are few, but among them they find the generosity and community spirit that has survived in the Highlands for generations. Working as a tight family unit, they learn to cope, and in time grow to love their little croft. As Neil Gunn writes in his Foreword, their lives gain extra dimensions that 'give the book its unusual quality, its brightness, and its wisdom'.

Show book

SIMPLE Secrets: Transforming...

Eamon Ravenscroft

SIMPLE Secrets: Transforming Your Wealth Beyond Traditional Banking
Are you eager to elevate your financial acumen and master the transformative potential of Bitcoin and other modern financial strategies?
If you’re in search of a thorough guide that encompasses all the crucial elements for unlocking financial wisdom, your quest ends here!
This guide is your essential resource for deepening your understanding, honing your skills, and engaging in practical exercises. With this comprehensive framework, you are set for financial success.
Updated for the Latest Financial Landscape.
Key Highlights of this Comprehensive Guide:
- In-depth insights into the world of innovative financial strategies
- Detailed explanations of Bitcoin and its transformative potential
- Effective strategies for financial education and application
Our guide stands out with its extensive coverage, critical for achieving your financial goals. Concepts are explored in depth, ensuring clarity and comprehension.
Please note that this guide is an independent resource not affiliated with any official financial institution, designed solely for your benefit.
Crafted with a logical structure and accessible language, our guide ensures seamless transitions between topics. Bid farewell to convoluted jargon and embrace clear, concise, and technically accurate content.
So, why hesitate? Click the BUY NOW button, secure your copy, and embark on your journey to financial mastery today!
Start transforming your financial future now!

Show book