Symplectic U7, U8 and U9 singularities

• Autorzy: Trębska Ż.
• Języki publikacji: EN

Abstrakty

EN

We use the method of algebraic restrictions to classify symplectic U7, ;U8 and U9 singularities. We use discrete symplectic invariants to distinguish symplectic singularities of the curves. We also give the geometric description of symplectic classes.

Słowa kluczowe

EN

symplectic manifold; curves; local symplectic algebra; algebraic restrictions; relative Darboux theorem; singularities; discrete sympletic invariants

PL

krzywe; algebra lokalna symplektyczna; twierdzenie Darboux'a; osobliwości

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2015
• Tom: Vol. 48, nr 2
• Strony: 322--347
• Opis fizyczny: Bibliogr. 18 poz., tab.

Twórcy

autor

Trębska Ż.

• Warsaw University of Technology, Faculty of Mathematics and Information Science, Koszykowa 75, 00-662 Warszawa, Poland

Bibliografia

• [1] V. I. Arnold, First steps of local contact algebra, Canad. J. Math. 51(6) (1999), 1123–1134.
• [2] V. I. Arnold, First step of local symplectic algebra, Differential topology, infinitedimensional Lie algebras, and applications, D. B. Fuchs’ 60th anniversary collection, Amer. Math. Soc. Transl. Ser. 2 194(44) (1999), 1–8.
• [3] V. I. Arnold, A. B. Givental, Symplectic geometry, in Dynamical Systems, IV, 1–138, Encyclopedia of Matematical Sciences, vol. 4, Springer, Berlin, 2001.
• [4] V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko, Singularities of Differentiable Maps, vol. 1, Birhauser, Boston, 1985.
• [5] W. Domitrz, Local symplectic algebra of quasi-homogeneous curves, Fund. Math. 204 (2009), 57–86.
• [6] W. Domitrz, Zero-dimensional symplectic isolated complete intersection singularities, Journal of Singularities 6 (2012), 19–26.
• [7] W. Domitrz, S. Janeczko, M. Zhitomirskii, Relative Poincare lemma, contractibility, quasi-homogeneity and vector fields tangent to a singular variety, Illinois J. Math. 48(3) (2004), 803–835.
• [8] W. Domitrz, S. Janeczko, M. Zhitomirskii, Symplectic singularities of varietes: the method of algebraic restrictions, J. Reine Angew. Math. 618 (2008), 197–235.
• [9] W. Domitrz, J. H. Rieger, Volume preserving subgroups of A and K and singularities in unimodular geometry, Math. Ann. 345 (2009), 783–817.
• [10] W. Domitrz, Ż. Trębska, Symplectic T7, T8 singularities and Lagrangian tangency orders, Proc. Edinb. Math. Soc. 55(3) (2012), 657–683.
• [11] W. Domitrz, Ż. Trębska, Symplectic Sμ singularities, Real and Complex Singularities, Contemporary Mathematics, Amer. Math. Soc., Providence, RI 569 (2012), 45–65.
• [12] M. Giusti, Classification des singularités isolées d’intersections complètes simples, C. R. Acad. Sci. Paris Sér. A 284 (1977), 167–170.
• [13] G. Ishikawa, S. Janeczko, Symplectic bifurcations of plane curves and isotropic liftings, Q. J. Math. 54(1) (2003), 73–102.
• [14] G. Ishikawa, S. Janeczko, Symplectic singularities of isotropic mappings, Geometric Singularity Theory, Banach Center Publ. vol. 65, 2004, 85–106.
• [15] P. A. Kolgushkin, Classification of simple multigerms of curves in a space endowed with a symplectic structure, St. Petersburg Math. J. 15(1) (2004), 103–126.
• [16] E. J. M. Looijenga, Isolated Singular Points on Complete Intersections, London Mathematical Society Lecture Note Series 77, Cambridge University Press, 1984.
• [17] Ż. Trębska, Symplectic W8 and W9 singularities, Journal of Singularities 6 (2012), 158–178
• [18] M. Zhitomirskii, Relative Darboux theorem for singular manifolds and local contact algebra, Canad. J. Math. 57(6) (2005), 1314–1340.