Elliptic K3 surfaces as dynamical models and their Hamiltonian monodromy

Daisuke Tarama

Open Mathematics (2012)

  • Volume: 10, Issue: 5, page 1619-1626
  • ISSN: 2391-5455

Abstract

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This note deals with Lagrangian fibrations of elliptic K3 surfaces and the associated Hamiltonian monodromy. The fibration is constructed through the Weierstraß normal form of elliptic surfaces. There is given an example of K3 dynamical models with the identity monodromy matrix around 12 elementary singular loci.

How to cite

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Daisuke Tarama. "Elliptic K3 surfaces as dynamical models and their Hamiltonian monodromy." Open Mathematics 10.5 (2012): 1619-1626. <http://eudml.org/doc/269278>.

@article{DaisukeTarama2012,
abstract = {This note deals with Lagrangian fibrations of elliptic K3 surfaces and the associated Hamiltonian monodromy. The fibration is constructed through the Weierstraß normal form of elliptic surfaces. There is given an example of K3 dynamical models with the identity monodromy matrix around 12 elementary singular loci.},
author = {Daisuke Tarama},
journal = {Open Mathematics},
keywords = {K3 dynamical model; Completely integrable system; Lagrangian fibration; Elliptic K3 surface; Monodromy; completely integrable system; elliptic K3 surface; monodromy},
language = {eng},
number = {5},
pages = {1619-1626},
title = {Elliptic K3 surfaces as dynamical models and their Hamiltonian monodromy},
url = {http://eudml.org/doc/269278},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Daisuke Tarama
TI - Elliptic K3 surfaces as dynamical models and their Hamiltonian monodromy
JO - Open Mathematics
PY - 2012
VL - 10
IS - 5
SP - 1619
EP - 1626
AB - This note deals with Lagrangian fibrations of elliptic K3 surfaces and the associated Hamiltonian monodromy. The fibration is constructed through the Weierstraß normal form of elliptic surfaces. There is given an example of K3 dynamical models with the identity monodromy matrix around 12 elementary singular loci.
LA - eng
KW - K3 dynamical model; Completely integrable system; Lagrangian fibration; Elliptic K3 surface; Monodromy; completely integrable system; elliptic K3 surface; monodromy
UR - http://eudml.org/doc/269278
ER -

References

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  9. [9] Kodaira K., On compact analytic surfaces: I, II, III, Ann. of Math., 1960, 71, 111–152; 1963, 77, 563-626; 1963, 78, 1–40 http://dx.doi.org/10.2307/1969881 Zbl0098.13004
  10. [10] Leung N.C., Symington M., Almost toric symplectic four-manifolds, J. Symplectic Geom., 2010, 8(2), 143–187 Zbl1197.53103
  11. [11] Markushevich D.G., Integrable symplectic structures on compact complex manifolds, Math. USSR-Sb., 1988, 59(2), 459–469 http://dx.doi.org/10.1070/SM1988v059n02ABEH003146 Zbl0637.58004
  12. [12] Pjateckiĭ-Šapiro I.I., Šafarevič I.R., A Torelli theorem for algebraic surfaces of type K3, Math. USSR Izvestija, 1971, 5(3), 547–588 http://dx.doi.org/10.1070/IM1971v005n03ABEH001075 
  13. [13] Zhilinskií B., Quantum monodromy and pattern formation, 2010, J. Phys. A, 43, #434033 http://dx.doi.org/10.1088/1751-8113/43/43/434033 Zbl1202.81100

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