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

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

In fresh years, study in K3 surfaces and Calabi–Yau types has visible fabulous growth from either mathematics and geometric issues of view, which in flip maintains to have an enormous impression 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 provide a state of the art survey of those new advancements. This complaints quantity contains a consultant sampling of the wide diversity of issues coated by means of the workshop. whereas the topics variety from mathematics geometry via algebraic geometry and differential geometry to mathematical physics, the papers are evidently similar by way of the typical subject matter of Calabi–Yau kinds. With the wide range of branches of arithmetic and mathematical physics touched upon, this zone unearths 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 kick off point for the graduate scholars and different junior researchers, or as a consultant to the topic.

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

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This is impossible because δ ∈ L− X. For r ∈ L− with r2 = −2, we define r⊥ = {[ω] ∈ D(L− ) : ω, r = 0}, r⊥ H= r K3 and Enriques Surfaces 13 where r belongs to the set of vectors in L− with r2 = −2. 3 implies that the periods of Enriques surfaces lie in D(L− )\H, and in fact, the moduli space of Enriques surfaces is given by (D(L− ) \ H)/Γ. It is known that H/Γ is irreducible. H is called the discriminant locus of Enriques surfaces. The Torelli type theorem for Enriques surfaces was first given by Horikawa [18].

Acknowledgements The author was supported in part by JSPS Grant-in-Aid (S), No. 22224001, No. 19104001. K3 and Enriques Surfaces 27 References 1. D. Allcock, E. Freitag, Cubic surfaces and Borcherds products. Comment. Math. Helv. 77, 270–296 (2002) 2. W. Barth, C. Peters, Automorphisms of Enriques surfaces. Invent. Math. 73, 383–411 (1983) 3. W. Barth, K. Hulek, C. Peters, A. Van de Ven, Compact Complex Surfaces, 2nd edn. (Springer, Berlin, 2003) 4. R. Borcherds, Automorphism groups of Lorentzian lattices.

S. Kond¯o, The moduli space of 8 points on P1 and automorphic forms. Contemp. Math. 422, 89–106 (2007) 27. S. Kond¯o, Moduli of plane quartics, G¨opel invariants and Borcherds products. Int. Math. Res. Notices 2011, 2825–2860 (2011) 28. S. Mukai, Finite groups of automorphisms of K3 surfaces and the Mathieu group. Invent. Math. 94, 183–221 (1988) 28 S. Kond¯o 29. V. Nikulin, Finite groups of automorphisms of K¨ahlerian surfaces of type K3. Moscow Math. Soc. 38, 71–137 (1980) 30. V. Nikulin, Integral symmetric bilinear forms and its applications.

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