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Trudy Mat. Inst. Steklova, 1999, Volume 225, Pages 132–152 (Mi tm716)  

This article is cited in 13 scientific papers (total in 13 papers)

How to Calculate Homology Groups of Spaces of Nonsingular Algebraic Projective Hypersurfaces

V. A. Vassiliev


Abstract: A general method of computing cohomology groups of the space of nonsingular algebraic hypersurfaces of degree $d$ in $\mathbf{CP}^n$ is described. Using this method, rational cohomology groups of such spaces with $n=2$, $d\le 4$ and $n=3=d$ and also of the space of nondegenerate quadratic vector fields in $\mathbf C^3$ are calculated.

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English version:
Proceedings of the Steklov Institute of Mathematics, 1999, 225, 121–140

Bibliographic databases:
UDC: 515.14+512.7
Received in December 1998

Citation: V. A. Vassiliev, “How to Calculate Homology Groups of Spaces of Nonsingular Algebraic Projective Hypersurfaces”, Solitons, geometry, and topology: on the crossroads, Collection of papers dedicated to the 60th anniversary of academician Sergei Petrovich Novikov, Trudy Mat. Inst. Steklova, 225, Nauka, MAIK Nauka/Inteperiodika, M., 1999, 132–152; Proc. Steklov Inst. Math., 225 (1999), 121–140

Citation in format AMSBIB
\Bibitem{Vas99}
\by V.~A.~Vassiliev
\paper How to Calculate Homology Groups of Spaces of Nonsingular Algebraic Projective Hypersurfaces
\inbook Solitons, geometry, and topology: on the crossroads
\bookinfo Collection of papers dedicated to the 60th anniversary of academician Sergei Petrovich Novikov
\serial Trudy Mat. Inst. Steklova
\yr 1999
\vol 225
\pages 132--152
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm716}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1725936}
\zmath{https://zbmath.org/?q=an:0981.55008}
\transl
\jour Proc. Steklov Inst. Math.
\yr 1999
\vol 225
\pages 121--140


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Das R., “The Space of Cubic Surfaces Equipped With a Line”, Math. Z.  crossref  isi
    2. Vassiliev V.A., “Homology of spaces of knots in any dimensions”, Philosophical Transactions of the Royal Society of London Series A–Mathematical Physical and Engineering Sciences, 359:1784 (2001), 1343–1364  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    3. Vassiliev V., “Resolutions of discriminants and topology of their complements”, New Developments in Singularity Theory, NATO Science Series, Series II: Mathematics, Physics and Chemistry, 21, 2001, 87–115  mathscinet  zmath  isi
    4. C. A. M. Peters, J. H. M. Steenbrink, “Degeneration of the Leray spectral sequence for certain geometric quotients”, Mosc. Math. J., 3:3 (2003), 1085–1095  mathnet  crossref  mathscinet  zmath
    5. V. A. Vassiliev, “Spaces of Hermitian operators with simple spectra and their finite-order cohomology”, Mosc. Math. J., 3:3 (2003), 1145–1165  mathnet  crossref  mathscinet  zmath
    6. Gorinov A.G., “Conical resolutions of discriminant varieties and real cohomology of the space of nonsingular complex plane projective quintics”, Doklady Mathematics, 67:2 (2003), 259–262  mathscinet  zmath  isi
    7. Tommasi O., “Rational cohomology of the moduli space of genus 4 curves”, Compositio Mathematica, 141:2 (2005), 359–384  crossref  mathscinet  zmath  isi  scopus  scopus
    8. de Bobadilla J.F., “Moduli spaces of polynomials in two variables”, Memoirs of the American Mathematical Society, 173:817 (2005), VII  mathscinet  isi
    9. Tommasi O., “Rational cohomology of M–3,M–2”, Compositio Mathematica, 143:4 (2007), 986–1002  crossref  mathscinet  zmath  isi  scopus
    10. Bergstrom J., Tommasi O., “The rational cohomology of (M)over–bar(4)”, Mathematische Annalen, 338:1 (2007), 207–239  crossref  mathscinet  zmath  isi  scopus  scopus
    11. V. A. Vassiliev, “Rational homology of the order complex of zero sets of homogeneous quadratic polynomial systems in $\mathbb R^3$”, Proc. Steklov Inst. Math., 290:1 (2015), 197–209  mathnet  crossref  crossref  isi  elib  elib
    12. V. A. Vassiliev, “Homology groups of spaces of non-resultant quadratic polynomial systems in ${\mathbb R}^3$”, Izv. Math., 80:4 (2016), 791–810  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    13. Gomez-Gonzales C., “Spaces of Non-Degenerate Maps Between Complex Projective Spaces”, Res. Math. Sci., 7:3 (2020), 26  crossref  isi
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