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Elliptic surfaces play a prominent role in the classification of algebraic surfaces and fit well within the general theory. In fact, they admit relatively simple foundations which in particular do not require too many prerequisites. Yet elliptic surfaces are endowed with many different applications for several areas of research, such as lattice theory, singularities, group theory, and modular curves. Our aim is to present some recent advances in studying the structure of parameter (or moduli) spaces of elliptic surfaces. We introduce a combinatorial description which involves special graphs...

Algebraic curves have many special properties that make their study particularly rewarding. As a result, curves provide a natural introduction to algebraic geometry. In this book, the authors also bring out certain aspects of curves and emphasize connections with algebra. This text covers the essential topics in the geometry of algebraic curves, such as line and vector bundles, the Riemann-Roch Theorem, divisors, coherent sheaves, and zeroth and first cohomology groups. The authors make a point of using concrete examples and explicit methods to ensure that the style is clear and...