“…This book will be particularly useful for graduate students and researchers interested in the connections between algebraic geometry and number theory. The prerequisites are some knowledge of number theory and algebraic geometry.…”
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“…The space of all Riemann surfaces (the so-called moduli space) plays an important role in algebraic geometry and its applications to quantum field theory. …”
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“…The reader should have some familiarity with commutative algebra and algebraic geometry.…”
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“…Lately, however, coding theorists have added techniques from algebraic geometry to their toolboxes. In particular, by re-interpreting the Reed-Solomon codes, one can see how to define new codes based on divisors on algebraic curves. …”
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“…Homogeneous spaces of linear algebraic groups lie at the crossroads of algebraic geometry, theory of algebraic groups, classical projective and enumerative geometry, harmonic analysis, and representation theory. …”
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“…Bogomolov: The theory of invariants and its applications to some problems in the algebraic geometry.- E. Bombieri: Methods of algebraic geometry in Char. …”
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“…A polarised variety is a modern generalization of the notion of a variety in classical algebraic geometry. It consists of a pair: the algebraic variety itself, together with an ample line bundle on it. …”
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“…The conjectural theory of mixed motives would be a universal cohomology theory in arithmetic algebraic geometry. The monograph describes the approach to motives via their well-defined realizations. …”
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“…This book should be of interest to graduate students and researchers in the field of algebraic geometry. The reader is expected to have some basic knowledge of enumerative algebraic geometry and pointwise Hilbert schemes.…”
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“…By giving a taste of the main ideas in the field, the author welcomes new readers to this exciting area at the crossroads of topology, algebraic geometry, analysis, and differential equations. …”
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“…It constitutes an accessible yet swift introduction to a new and active area within algebraic geometry, which connects well with classical intersection theory. …”
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“…Advances in this field often result from mixing sophisticated techniques from algebraic geometry, lattice theory, number theory, and dynamical systems. …”
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“…It includes the elementary facts of algebraic geometry indispensable for its understanding. …”
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“…The book is suitable for use as a text for a topics course in algebraic geometry; includes an appendix by B. Brent Gordon.…”
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“…Motivated by engineering vector-like (Higgs) pairs in the spectrum of 4d F-theory compactifications, we combine machine learning and algebraic geometry techniques to analyze line bundle cohomologies on families of holomorphic curves. …”
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“…Both authors are well-known researchers and the second, Manin, is famous for his work in algebraic geometry and mathematical physics. The book is an excellent reference for graduate students and researchers in mathematics and also for physicists who use methods from algebraic geometry and algebraic topology.…”
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“…Researchers in non-commutative algebraic geometry, control theory, system engineering, optimization, quantum physics and information science will find the unified notation and mixture of algebraic geometry and mathematical programming useful. …”
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“…Algebraic geometry is often employed to encode and decode signals transmitted in communication systems. …”
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“…It contains four chapters which discuss homology theory in an abelian category together with some important and fundamental applications in geometry, topology, algebraic geometry (including basics in abstract algebraic geometry), and group theory. …”
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“…Over the last few decades, this notion has become central not only in algebraic geometry, but in mathematical physics, including string theory, as well. …”
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