Arithmetic and Geometry of K3 Surfaces and Calabi–Yau by Shigeyuki Kondō (auth.), Radu Laza, Matthias Schütt, Noriko

By Shigeyuki Kondō (auth.), Radu Laza, Matthias Schütt, Noriko Yui (eds.)

In fresh years, study in K3 surfaces and Calabi–Yau kinds has obvious fabulous development from either mathematics and geometric issues of view, which in flip keeps to have an incredible effect and impression in theoretical physics—in specific, in string thought. 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 contains a consultant sampling of the wide diversity of themes lined by way of the workshop. whereas the themes variety from mathematics geometry via algebraic geometry and differential geometry to mathematical physics, the papers are obviously similar via the typical subject matter of Calabi–Yau types. With the wide variety of branches of arithmetic and mathematical physics touched upon, this zone finds many deep connections among topics 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 kick off point for the graduate scholars and different junior researchers, or as a advisor to the topic.

Show description

Read Online or Download Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds PDF

Best geometry books

Gems of Geometry

In accordance with a sequence of lectures for grownup scholars, this vigorous and unique publication proves that, faraway from being a dusty, uninteresting topic, geometry is actually filled with good looks and fascination. The author's infectious enthusiasm is placed to exploit in explaining a number of the key techniques within the box, beginning with the Golden quantity and taking the reader on a geometric trip through Shapes and Solids, in the course of the Fourth measurement, winding up with Einstein's Theories of Relativity.

Pi: A Source Book

Pi is likely one of the few thoughts in arithmetic whose point out conjures up a reaction of popularity and curiosity in these now not involved professionally with the topic. but, regardless of this, no resource e-book on Pi has ever been released. Mathematicians and historians of arithmetic will locate this publication critical.

Low Dimensional Topology

Derived from a unique consultation on Low Dimensional Topology equipped and performed via Dr Lomonaco on the American Mathematical Society assembly held in San Francisco, California, January 7-11, 1981

Extra info for Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds

Example text

Hence x ∈ S ⊕ T . This implies the injectivity of pS |H. Similarly pT |H is injective. Since |H|2 = |AS | · |AT |, pS |H and pT |H are isomorphic. The remaining assertions are obvious. Conversely we have the following corollary. 12 Corollary Let S , T be even lattices. Let γ : AS → AT be an isomorphism satisfying qT (γ(x)) ≡ −qS (x) mod 2 for any x ∈ AS . Then there exist an even unimodular lattice L and K3 and Enriques Surfaces 9 a primitive embedding of S into L such that T is isomorphic to the orthogonal complement of S in L.

Hence h preserves both the Hodge and complexified weight filtrations. Now use the fact that A ⊗ Q is a field to deduce that h preserves the weight filtration over A ⊗ Q. 1 Transcendental Methods in the Study of Algebraic Cycles. . 13. Let U be a compact Riemann surface, Σ ⊂ U a finite set of points, and put U := U\Σ. According to Deligne, H 1 (U, Z(1)) carries a Z-MHS. The Hodge filtration on H 1 (U, C) is defined in terms of a filtered complex of holomorphic differentials on U with logarithmic poles along Σ ([16], but also see (10) below).

N>0 Then we have a holomorphic automorphic form Ψ12 on D(L) of weight 12 = 24/2 with zeros along λ⊥ . λ∈L, λ2 =−2 In the following we discuss some applications of Ψ12 to the moduli spaces of polarized K3 surfaces. 5). Consider the last component E8 in the above decomposition of L, and let x ∈ E8 be a primitive vector with x2 = −2d. Let R be the orthogonal complement of x in E8 . Then R⊥ = U ⊕ U ⊕ E8 ⊕ E8 ⊕ (−2d) L2d where (−2d) is the lattice generated by x. Thus we have a primitive embedding of L2d into L which induces an embedding of the period domain D2d of polarized K3 surfaces of degree 2d into D(L).

Download PDF sample

Rated 5.00 of 5 – based on 30 votes