SMOOTHINGS OF SINGULARITIES AND SYMPLECTIC TOPOLOGY

Date

2013-01-01

Author

Bhupal, Mohan Lal

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

185
views

0
downloads

We review the symplectic methods which have been applied in the classification of weighted homogeneous singularities with rational homology disk (QHD) smoothings. We also review the construction of such smoothings and show that in many cases these smoothings are unique up to symplectic deformation. In addition, we describe a method for finding differential topological descriptions (more precisely, Kirby diagrams) of the smoothings and illustrate this method by working out a family of examples.

URI

https://hdl.handle.net/11511/69968

Journal

DEFORMATIONS OF SURFACE SINGULARITIES

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

WEIGHTED HOMOGENEOUS SINGULARITIES AND RATIONAL HOMOLOGY DISK SMOOTHINGS Bhupal, Mohan Lal (2011-10-01) We classify the resolution graphs of weighted homogeneous surface singularities which admit rational homology disk smoothings. The nonexistence of rational homology disk smoothings is shown by symplectic geometric methods, while the existence is verified via smoothings of negative weight.
Geometric measures of entanglement UYANIK, KIVANÇ; Turgut, Sadi (American Physical Society (APS), 2010-03-01) The geometric measure of entanglement, which expresses the minimum distance to product states, has been generalized to distances to sets that remain invariant under the stochastic reducibility relation. For each such set, an associated entanglement monotone can be defined. The explicit analytical forms of these measures are obtained for bipartite entangled states. Moreover, the three-qubit case is discussed and it is argued that the distance to the W states is a new monotone.
Galois structure of modular forms of even weight Gurel, E. (Elsevier BV, 2009-10-01) We calculate the equivariant Euler characteristics of powers of the canonical sheaf on certain modular curves over Z which have a tame action of a finite abelian group. As a consequence, we obtain information on the Galois module structure of modular forms of even weight having Fourier coefficients in certain ideals of rings of cyclotomic algebraic integers. (c) 2009 Elsevier Inc. All rights reserved.
DEFORMATION CLASSES OF REAL FOUR-DIMENSIONAL CUBIC HYPERSURFACES Finashin, Sergey (2008-10-01) We study real nonsingular cubic hypersurfaces X subset of P-5 up to deformation equivalence combined with projective equivalence and prove that, they, are classified by the conjugacy classes of involutions induced by the complex conjugation in H-4(X). Moreover, we provide a graph Gamma(K4) whose vertices represent the equivalence classes of such cubics and whose edges represent their adjacency. It turns out that the graph Gamma(K4) essentially coincides with the graph Gamma(K3) characterizing a certain adja...
Frequency estimation of a single real-valued sinusoid: An invariant function approach Candan, Çağatay; Çelebi, Utku (2021-08-01) An invariant function approach for the computationally efficient (non-iterative and gridless) maximum likelihood (ML) estimation of unknown parameters is applied on the real-valued sinusoid frequency estimation problem. The main attraction point of the approach is its potential to yield a ML-like performance at a significantly reduced computational load with respect to conventional ML estimator that requires repeated evaluation of an objective function or numerical search routines. The numerical results ind...

Citation Formats

M. L. Bhupal, “SMOOTHINGS OF SINGULARITIES AND SYMPLECTIC TOPOLOGY,” DEFORMATIONS OF SURFACE SINGULARITIES, pp. 57–97, 2013, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/69968.