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

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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 1999, Volume 225, Pages 132–152 (Mi tm716)

This article is cited in 15 scientific papers (total in 15 papers)

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

V. A. Vassiliev

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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.

Received in December 1998

Bibliographic databases:

Document Type: Article

UDC: 515.14+512.7

Language: Russian

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://mathscinet.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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https://www.mathnet.ru/eng/tm716

https://www.mathnet.ru/eng/tm/v225/p132

This publication is cited in the following 15 articles:

Das R., “Cohomology of the Universal Smooth Cubic Surface”, BJS Open, 6:1 (2022), 795–815
Das R., “The Space of Cubic Surfaces Equipped With a Line”, Math. Z., 298:1-2 (2021), 653–670
Zheng A., “Rational Cohomology of the Moduli Space of Trigonal Curves of Genus 5”, Manuscr. Math., 2021
Gomez-Gonzales C., “Spaces of Non-Degenerate Maps Between Complex Projective Spaces”, Res. Math. Sci., 7:3 (2020), 26
V. A. Vassiliev, “Homology groups of spaces of non-resultant quadratic polynomial systems in ${\mathbb R}^3$”, Izv. Math., 80:4 (2016), 791–810
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
Tommasi O., “Rational cohomology of M–3,M–2”, Compositio Mathematica, 143:4 (2007), 986–1002
Bergstrom J., Tommasi O., “The rational cohomology of (M)over–bar(4)”, Mathematische Annalen, 338:1 (2007), 207–239
Tommasi O., “Rational cohomology of the moduli space of genus 4 curves”, Compositio Mathematica, 141:2 (2005), 359–384
de Bobadilla J.F., “Moduli spaces of polynomials in two variables”, Memoirs of the American Mathematical Society, 173:817 (2005), VII
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
V. A. Vassiliev, “Spaces of Hermitian operators with simple spectra and their finite-order cohomology”, Mosc. Math. J., 3:3 (2003), 1145–1165
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
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
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

Citing articles in Google Scholar: Russian citations, English citations
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Труды Математического института имени В. А. Стеклова

Proceedings of the Steklov Institute of Mathematics

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