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

February 1, 2018 | Geometry | By admin | 0 Comments

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

ISBN-10: 1461464021

ISBN-13: 9781461464020

ISBN-10: 146146403X

ISBN-13: 9781461464037

In contemporary years, examine in K3 surfaces and Calabi–Yau forms has obvious awesome development from either mathematics and geometric issues of view, which in flip maintains to have a big effect and impression in theoretical physics—in specific, in string idea. The workshop on mathematics and Geometry of K3 surfaces and Calabi–Yau threefolds, held on the Fields Institute (August 16-25, 2011), aimed to provide a state of the art survey of those new advancements. This complaints quantity incorporates a consultant sampling of the wide diversity of issues lined through the workshop. whereas the themes variety from mathematics geometry via algebraic geometry and differential geometry to mathematical physics, the papers are evidently similar via the typical subject of Calabi–Yau forms. With the wide range of branches of arithmetic and mathematical physics touched upon, this quarter finds many deep connections among matters formerly thought of unrelated.

Unlike so much different meetings, the 2011 Calabi–Yau workshop all started with three days of introductory lectures. a variety of four of those lectures is incorporated during this quantity. those lectures can be utilized as a place to begin for the graduate scholars and different junior researchers, or as a advisor to the topic.

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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).

20 S. Kond¯o Next we consider finite groups of symplectic automorphisms. We start with the following proposition. 10 Proposition ([29]) (1) Let g be a finite symplectic automorphism of a K3 surface. Then |g| ≤ 8. (2) g has only isolated fixed points and the number of fixed points depends only on the order of g. (3) Let g be of order m and let fm be the number of fixed points of g. Then fm is given in the following Table 3. Table 3: The number of fixed points of finite symplectic automorphisms of K3 surfaces m2345678 fm 8 6 4 4 2 3 2 Recall that the Mathieu group M24 acts on the set Ω = {1, .

J. 195, 165–186 (2009) 35. I. R. Shafarevich, A Torelli theorem for algebraic surfaces of type K3. USSR Izv. 35, 530–572 (1971) 36. B. Segre, The Non-singular Cubic Surfaces (Oxford, Oxford University Press 1942) 37. P. Serre, in A Course in Arithmetic, 3rd edn. Grundlehren Math. , Bd 290 (Springer, Berlin, 1999) 38. B. Vinberg, The two most algebraic K3 surfaces. Math. Ann. 265, 1–21 (1983) 39. B. Vinberg, Classification of 2-reflective hyperbolic lattices of rank 4. Trans. Moscow Math. Soc. 68, 39–66 (2007) Transcendental Methods in the Study of Algebraic Cycles with a Special Emphasis on Calabi–Yau Varieties James D.

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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.)

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