Symplectic topology of $K3$ surfaces via mirror symmetry

Abstract We continue our study on the hypergeometric system $E(3,6)$ that describes period integrals of the double cover family of K3 surfaces. Near certain special boundary points in the moduli space of the K3 surfaces, we construct the local solutions and determine the so-called mirror maps expressing them in terms of genus 2 theta functions. These mirror maps are the K3 analogues of the elliptic $\lambda $-function. We find that there are two nonisomorphic definitions of the lambda functions corresponding to a flip in the moduli space. We also discuss mirror symmetry for the double cover K3 surfaces and their higher dimensional generalizations. A follow-up paper will describe more details of the latter.

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Mirror symmetry for K3 surfaces

Geometriae Dedicata ◽

10.1007/s10711-020-00548-0 ◽

2020 ◽

Author(s):

C. J. Bott ◽

Paola Comparin ◽

Nathan Priddis

Keyword(s):

Mirror Symmetry ◽

K3 Surfaces

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The Berglund–Hübsch–Chiodo–Ruan mirror symmetry for K3 surfaces

Journal de Mathématiques Pures et Appliquées ◽

10.1016/j.matpur.2014.02.005 ◽

2014 ◽

Vol 102 (4) ◽

pp. 758-781 ◽

Cited By ~ 8

Author(s):

Michela Artebani ◽

Samuel Boissière ◽

Alessandra Sarti

Keyword(s):

Mirror Symmetry ◽

K3 Surfaces

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K3 surfaces, Lorentzian Kac–Moody algebras and Mirror Symmetry

Mathematical Research Letters ◽

10.4310/mrl.1996.v3.n2.a7 ◽

1996 ◽

Vol 3 (2) ◽

pp. 211-229 ◽

Cited By ~ 19

Author(s):

Valeri A. Gritsenko ◽

Viacheslav V. Nikulin

Keyword(s):

Mirror Symmetry ◽

K3 Surfaces

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Categorial Mirror Symmetry for K3 Surfaces

Communications in Mathematical Physics ◽

10.1007/s002200050705 ◽

1999 ◽

Vol 206 (2) ◽

pp. 265-272 ◽

Cited By ~ 2

Author(s):

C. Bartocci ◽

U. Bruzzo ◽

G. Sanguinetti

Keyword(s):

Mirror Symmetry ◽

K3 Surfaces

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Mirror Symmetry on K3 Surfaces via Fourier-Mukai Transform

Communications in Mathematical Physics ◽

10.1007/s002200050380 ◽

1998 ◽

Vol 195 (1) ◽

pp. 79-93 ◽

Cited By ~ 13

Author(s):

Claudio Bartocci ◽

Ugo Bruzzo ◽

Daniel Hernández Ruipérez ◽

José M. Muñoz Porras

Keyword(s):

Mirror Symmetry ◽

K3 Surfaces

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The mirror symmetry of K3 surfaces with non-symplectic automorphisms of prime order

Advances in Theoretical and Mathematical Physics ◽

10.4310/atmp.2014.v18.n6.a4 ◽

2014 ◽

Vol 18 (6) ◽

pp. 1335-1368 ◽

Cited By ~ 5

Author(s):

Paola Comparin ◽

Christopher Lyons ◽

Nathan Priddis ◽

Rachel Suggs

Keyword(s):

Mirror Symmetry ◽

Prime Order ◽

K3 Surfaces ◽

Symplectic Automorphisms

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PERTURBATIVE DEFORMATIONS OF CONFORMAL FIELD THEORIES REVISITED

Reviews in Mathematical Physics ◽

10.1142/s0129055x10003916 ◽

2010 ◽

Vol 22 (02) ◽

pp. 117-192

Author(s):

IGOR KRIZ

Keyword(s):

Field Theory ◽

Conformal Field Theory ◽

Mirror Symmetry ◽

Free Field ◽

K3 Surfaces ◽

Point Of View ◽

Field Theories ◽

Conformal Field Theories ◽

Conformal Field ◽

Gepner Model

The purpose of this paper is to revisit the theory of perturbative deformations of conformal field theory from a mathematically rigorous, purely worldsheet point of view. We specifically include the case of N = (2,2) conformal field theories. From this point of view, we find certain surprising obstructions, which appear to indicate that contrary to previous findings, not all deformations along marginal fields exist perturbatively. This includes the case of deformation of the Gepner model of the Fermat quintic along certain cc fields. In other cases, including Gepner models of K3-surfaces and the free field theory, our results coincides with known predictions. We give partial interpretation of our results via renormalization and mirror symmetry.

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