92
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

CW Complexes for Complex Algebraic Surfaces

Pages 413-419 | Received 30 Jul 2010, Accepted 24 Aug 2010, Published online: 23 Feb 2011

REFERENCES

  • Alberti , L. , Mourrain , B. and Técourt , J.-P. 2009 . “Isotopic Triangulation of a Real Algebraic Surface.” . J. Symbolic Comput. , 44 ( 9 ) : 1291 – 1310 . [Alberti et al. 09]
  • Berberich , E. , Kerber , M. and Sagraloff , M. 2010 . “An Efficient Algorithm for the Stratification and Triangulation of an Algebraic Surface.” . Comput. Geom. , 43 ( 3 ) : 257 – 278 . [Berberich et al. 10]
  • Cheng , J.-S. , Gao , X.-S. and Li , M. 2005 . “Determining the Topology of Real Algebraic Surfaces.” . In Mathematics of Surfaces XI (Loughborough, 2005) 121 – 146 . Berlin : Springer. . Lect. Notes in Comput. Sci. 3604, [Cheng et al. 05]
  • Ciliberto , C. and Flamini , F. 2010 . “On the Branch Curve of a General Projection of a Surface to a Plane.” . Trans. Amer. Math. Soc. , To appear in, [Ciliberto and Flamini 10]
  • Collins , G. E. 1975 . “Quantifier Elimination for Real Closed Fields by Cylindrical Algebraic Decomposition.” . In Automata Theory and Formal Languages, 2nd GI Conference (Kaiserslautern, 1975) 134 – 183 . Berlin : Springer. . Lect. Notes in Comput. Sci. 33, [Collins 75]
  • DŁotko , P. , Kaczynski , T. , Mrozek , M. and Wanner , T. 2010 . “Coreduction Homology Algorithm for Regular CW-Complexes.” . Discrete Comput. Geom , To appear in, [DŁotko et al. 10]
  • Donald , B. R. and Chang , D. R. “On the Complexity of Computing the Homology Type of a Triangulation.” . Proceedings of the 32nd Annual IEEE Symposium on Foundations of Computer Science . 1991 , San Juan, PR. pp. 650 – 661 . Los Alamitos : IEEE Comput. Soc. Press. . [Donald and Chang 91]
  • Fortuna , E. , Gianni , P. , Parenti , P. and Traverso , C. 2003 . “Algorithms to Compute the Topology of Orientable Real Algebraic Surfaces.” . J. Symbolic Comput. , 36 ( 3–4 ) : 343 – 364 . [Fortuna et al. 03]
  • Gompf , R. E. and Stipsicz , A. I. 1999 . 4-Manifolds and Kirby Calculus Providence : Amer. Math. Soc. . [Gompf and Stipsicz 99]
  • Gyulassy , A. , Bremer , P.-T. , Hamann , B. and Pascucci , V. 2008 . “A Practical Approach to Morse-Smale Complex Computation: Scalability and Generality.” . IEEE Trans. Visual. Comput. Graphics , 14 ( 6 ) : 1619 – 1626 . [Gyulassy et al. 08]
  • Jäger , G. 2003 . “Parallel Algorithms for Computing the Smith Normal Form of Large Matrices.” . In Recent Advances in Parallel Virtual Machine and Message Passing Interface (Venice, 2003) 170 – 179 . Berlin : Springer. . Lect. Notes in Comput. Sci. 2840, [Jäger 03]
  • Kannan , R. and Bachem , A. 1979 . “Polynomial Algorithms for Computing the Smith and Hermite Normal Forms of an Integer Matrix.” . SIAM J. Comput. , 8 ( 4 ) : 499 – 507 . [Kannan and Bachem 79]
  • Kerber , M. and Sagraloff , M. 2010 . “A Note on the Complexity of Real Algebraic Hypersurfaces.” Preprint, [Kerber and Sagraloff 10]
  • Mayer , A. L. 1972 . “Families of K-3 Surfaces.” . Nagoya Math. J. , 48 : 1 – 17 . [Mayer 72]
  • Moishezon , B. G. 1981 . “Stable Branch Curves and Braid Monodromies.” . In Algebraic Geometry (Chicago, Ill., 1980) 107 – 192 . Berlin : Springer. . Lect. Notes in Math. 862, [Moishezon 81]
  • Mrozek , M. and Batko , B. 2009 . “Coreduction Homology Algorithm.” . Discrete Comput. Geom. , 41 ( 1 ) : 96 – 118 . [Mrozek and Batko 09]
  • Mrozek , M. , Pilarczyk , P. and Żelazna , N. 2008 . “Homology Algorithm Based on Acyclic Subspace.” . Comput. Math. Appl. , 55 ( 11 ) : 2395 – 2412 . [Mrozek et al. 08]
  • Schwartz , J. T. and Sharir , M. 1983 . “On the ‘Piano Movers’ Problem, II: General Techniques for Computing Topological Properties of Real Algebraic Manifolds.” . Adv. in Appl. Math. , 4 ( 3 ) : 298 – 351 . [Schwartz and Sharir 83]
  • Várilly-Alvarado , A. and Viray , B. 2010 . “Failure of the Hasse Principle for Enriques Surfaces.” Preprint, [Várilly-Alvarado and Viray 10]
  • Whitney , H. 1944 . “The Self-Intersections of a Smooth n-Manifold in 2n-Space.” . Ann. of Math. (2) , 45 ( 2 ) : 220 – 246 . [Whitney 44]
  • Whitney , H. 1957 . Geometric Integration Theory Princeton : Princeton Univ. Press. . [Whitney 57]
  • Zariski , O. 1929 . “On the Problem of Existence of Algebraic Functions of Two Variables Possessing a Given Branch Curve.” . Amer. J. Math. , 51 ( 2 ) : 305 – 328 . [Zariski 29]

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.