By Shigeyuki Kondō (auth.), Radu Laza, Matthias Schütt, Noriko Yui (eds.)
In contemporary years, study in K3 surfaces and Calabi–Yau forms has noticeable miraculous growth from either mathematics and geometric issues of view, which in flip keeps to have a tremendous impact and influence in theoretical physics—in specific, in string concept. The workshop on mathematics and Geometry of K3 surfaces and Calabi–Yau threefolds, held on the Fields Institute (August 16-25, 2011), aimed to offer a state of the art survey of those new advancements. This lawsuits quantity encompasses a consultant sampling of the vast diversity of subject matters coated through the workshop. whereas the themes variety from mathematics geometry via algebraic geometry and differential geometry to mathematical physics, the papers are obviously similar by way of the typical topic of Calabi–Yau types. With the wide range of branches of arithmetic and mathematical physics touched upon, this region finds many deep connections among matters formerly thought of unrelated.
Unlike such a lot different meetings, the 2011 Calabi–Yau workshop began with three days of introductory lectures. a range of four of those lectures is integrated during this quantity. those lectures can be utilized as a place to begin for the graduate scholars and different junior researchers, or as a consultant to the topic.
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Extra resources for Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds
These Chow groups come equipped with various maps whose target space is a certain transcendental cohomology theory called Deligne cohomology. More precisely these maps are called regulators, from the higher cycle groups of S. D. ca R. Laza et al. D. Lewis clr,m : CHr (X, m) → HD2r−m X, A(r) , (1) where A ⊆ R is a subring, A(r) := A(2πi) is called the “Tate twist”, and as we will indicate below, some striking evidence that these regulator maps become highly interesting in the case where X is Calabi–Yau.
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Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds by Shigeyuki Kondō (auth.), Radu Laza, Matthias Schütt, Noriko Yui (eds.)