The DOI matches its Crossref record; 15 of the 15 references it cites were found in a registry or an index.
Affine Structures and Non-Archimedean Analytic Spaces
Open accessAbstract
In this paper we propose a way to construct an analytic space over a non-archimedean field, starting with a real manifold with an affine structure which has integral monodromy. Our construction is motivated by the junction of the Homological Mirror conjecture and the geometric Strominger-Yau-Zaslow conjecture. In particular, we glue from “flat pieces” an analytic K3 surface. As a byproduct of our approach we obtain an action of an arithmetic subgroup of the group SO(1, 18) by piecewise-linear transformations on the two-dimensional sphere S 2 equipped with naturally defined singular affine structure. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Cites
Mathematical Methods of Classical Mechanics
Arnold, V. I. (1989) · Graduate Texts in Mathematics · doi:10.1007/978-1-4757-2063-1 · Cited by 9,116
Foundations of Differential Geometry
Kobayashi, S., & Nomizu, K. (1963) · UCLA - Biblioteca de Ciencias y Tecnologia Felix Morales Bueno · Cited by 6,384
Mathematical Methods of Classical Mechanics
Arnold, V. I. (1978) · Graduate Texts in Mathematics · doi:10.1007/978-1-4757-1693-1 · Cited by 5,106
On the foundations of differential geometry
Rubio, R. (1964) · Časopis pro pěstování matematiky · doi:10.21136/cpm.1964.117506 · Cited by 1,959
Homological Algebra of Mirror Symmetry
Kontsevich, M. (1995) · Birkhäuser Basel eBooks · doi:10.1007/978-3-0348-9078-6_11 · Cited by 1,112
Self-citationStrominger, A., Yau, S., & Zaslow, E. (1996) · Cited by 946
Strominger, A., Yau, S.-T., & Zaslow, E. (1996) · Nuclear Physics B · doi:10.1016/0550-3213(96)00434-8 · Cited by 917
HOMOLOGICAL MIRROR SYMMETRY AND TORUS FIBRATIONS
KONTSEVICH, M., & SOIBELMAN, Y. (2001) · Symplectic Geometry and Mirror Symmetry · doi:10.1142/9789812799821_0007 · Cited by 380
Self-citationTorification and factorization of birational maps
Abramovich, D., Karu, K., Matsuki, K., & Włodarczyk, J. (2002) · Journal of the American Mathematical Society · doi:10.1090/s0894-0347-02-00396-x · Cited by 290
Large Complex Structure Limits of K3 Surfaces
Gross, M., & Wilson, P. M. H. (2000) · Journal of Differential Geometry · doi:10.4310/jdg/1090341262 · Cited by 242
Cited by
Cohomological Hall algebra, exponential Hodge structures and motivic Donaldson–Thomas invariants
Kontsevich, M., & Soibelman, Y. (2011) · Communications in Number Theory and Physics · doi:10.4310/cntp.2011.v5.n2.a1 · Cited by 369
Self-citationTropical geometry and its applications
Mikhalkin, G. (2007) · Proceedings of the International Congress of Mathematicians Madrid, August 22–30, 2006 · doi:10.4171/022-2/40 · Cited by 317
Metadata
- Authors
- Kontsevich, M., & Soibelman, Y.
- Venue
- Progress in Mathematics
- Publisher
- Birkhäuser Boston
- Published
- 2007-05-30
- Pages
- 321-385
- OpenAlex
- W2154785235
- Cited by
- 255
- References
- 15
- FWCI
- 31.85
- Type
- book chapter
- Language
- en
- Open access
- green
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