This monograph gives an exposition of Hodge theory, leading to three new proofs of a local Torelli theorem for curves and a proof for a smooth family of surfaces, threefolds, or fourfolds, whose cotangent map is a birational morphism.
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This memoir develops the spectral theory of the Lax operators of nonlinear Schrödinger-like partial differential equations with periodic boundary conditions. Their special curves, i.e., the common spectrum with the periodic shifts, are generically Riemann surfaces of infinite ge…
Arc schemes and singularities
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Type: Book
Arc schemes and singularities
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Type: Book
Arc schemes and singularities
0
Type: Book
"This title introduces the theory of arc schemes in algebraic geometry and singularity theory, with special emphasis on recent developments around the Nash problem for surfaces. The main challenges are to understand the global and local structure of arc schemes, and how they rel…
Arc schemes and singularities
0
Type: Book
"The Mordell conjecture (Faltings's theorem) is one of the most important achievements in Diophantine geometry, stating that an algebraic curve of genus at least two has only finitely many rational points. This book provides a self-contained and detailed proof of the Mordell con…
"Challenge: Can you find all the integers a, b, c satisfying 2a²+3b²=5c²? Looks simple, and there are in fact a number of easy solutions. But most of them turn out to be anything but obvious! There are infinitely many possibilities, and as any computer will tell you, each of a, …
"Challenge: Can you find all the integers a, b, c satisfying 2a²+3b²=5c²? Looks simple, and there are in fact a number of easy solutions. But most of them turn out to be anything but obvious! There are infinitely many possibilities, and as any computer will tell you, each of a, …
