Abstract
We study the quotient variety of the space of foliations on
Funding source: Conachyt
Award Identifier / Grant number: 284424
Funding statement: This work was supported by the CONACHyT under Grant 284424. The second author is supported with a postdoc position by CONAHCyT.
Acknowledgements
The authors would like to thank the referee for the valuable contributions that significantly improved the article.
References
[1]
C. R. Alcántara,
The good quotient of the semi-stable foliations of
[2]
C. R. Alcántara,
Foliations on
[3]
C. R. Alcántara,
Foliations on
[4] M. Brion, Equivariant cohomology and equivariant intersection theory, Representation Theories and Algebraic Geometry, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 514, Kluwer Academic, Dordrecht (1998), 1–37. 10.1007/978-94-015-9131-7_1Suche in Google Scholar
[5] M. Brunella, Birational Geometry of Foliations, Monogr. Mat., Instituto de Matemática Pura e Aplicada, Rio de Janeiro, 2000. Suche in Google Scholar
[6] A. Campillo and J. Olivares, A plane foliation of degree different from 1 is determined by its singular scheme, C. R. Acad. Sci. Paris Sér. I Math. 328 (1999), no. 10, 877–882. 10.1016/S0764-4442(99)80289-4Suche in Google Scholar
[7] S. Casalaina-Martin, S. Grushevsky, K. Hulek and R. Laza, Cohomology of the moduli space of cubic threefolds and its smooth models, Mem. Amer. Math. Soc. 282 (2023), no. 1395, 5–100. 10.1090/memo/1395Suche in Google Scholar
[8] D. Cerveau, J. Déserti, D. Garba Belko and R. Meziani, Géométrie classique de certains feuilletages de degré deux, Bull. Braz. Math. Soc. (N. S.) 41 (2010), no. 2, 161–198. 10.1007/s00574-010-0008-xSuche in Google Scholar
[9]
D. Cerveau and A. Lins Neto,
Irreducible components of the space of holomorphic foliations of degree two in
[10] I. V. Dolgachev, Classical Algebraic Geometry. A Modern View, Cambridge University, Cambridge, 2012. 10.1017/CBO9781139084437Suche in Google Scholar
[11] E. Esteves and M. Marchisio, Invariant theory of foliations of the projective plane, Rend. Circ. Mat. Palermo (2) 83 (2011), 175–188. Suche in Google Scholar
[12] M. Fortuna, Cohomology of the moduli space of non-hyperelliptic genus four curves, Ann. Inst. Fourier (Grenoble) 71 (2021), no. 2, 757–797. 10.5802/aif.3409Suche in Google Scholar
[13] W. Fulton, Algebraic Curves, Adv. Book Class., Addison-Wesley, Redwood City, 1989. Suche in Google Scholar
[14] X. Gómez-Mont, Universal families of foliations by curves, Singularités d’équations différentielles, Société Mathématique de France, Paris (1987), 109–129. Suche in Google Scholar
[15] X. Gómez-Mont and G. Kempf, Stability of meromorphic vector fields in projective spaces, Comment. Math. Helv. 64 (1989), no. 3, 462–473. 10.1007/BF02564687Suche in Google Scholar
[16] M. Goresky and R. MacPherson, Intersection homology theory, Topology 19 (1980), no. 2, 135–162. 10.1016/0040-9383(80)90003-8Suche in Google Scholar
[17] P. Griffiths and J. Harris, Principles of Algebraic Geometry, Wiley Class. Libr., John Wiley & Sons, New York, 2014. Suche in Google Scholar
[18] W. H. Hesselink, Desingularizations of varieties of nullforms, Invent. Math. 55 (1979), no. 2, 141–163. 10.1007/BF01390087Suche in Google Scholar
[19] D. Husemöller, Fibre Bundles, Grad. Texts in Math., Springer, Berlin, 1994. 10.1007/978-1-4757-2261-1Suche in Google Scholar
[20] J. P. Jouanolou, Équations de Pfaff algébriques, Lecture Notes in Math. 708, Springer, Berlin, 1979. 10.1007/BFb0063393Suche in Google Scholar
[21] F. Kirwan, Cohomology of Quotients in Symplectic and Algebraic Geometry, Math. Notes 31, Princeton University, Princeton, 1984. 10.1515/9780691214566Suche in Google Scholar
[22] F. Kirwan, Partial desingularisations of quotients of nonsingular varieties and their Betti numbers, Ann. of Math. (2) 122 (1985), no. 1, 41–85. 10.2307/1971369Suche in Google Scholar
[23] F. Kirwan, Rational intersection cohomology of quotient varieties, Invent. Math. 86 (1986), no. 3, 471–505. 10.1007/BF01389264Suche in Google Scholar
[24]
F. Kirwan and R. Lee,
The cohomology of moduli spaces of
[25] F. Kirwan and J. Woolf, An Introduction to Intersection Homology Theory, 2nd ed., Chapman & Hall/CRC, Boca Raton, 2006. 10.1201/9780367800840Suche in Google Scholar
[26] L. G. Maxim, Intersection Homology & Perverse Sheaves—with Applications to Singularities, Grad. Texts in Math. 281, Springer, Cham 2019. 10.1007/978-3-030-27644-7Suche in Google Scholar
[27] D. Mumford, J. Fogarty and F. Kirwan, Geometric Invariant Theory, Ergeb. Math. Grenzgeb. (2) 34, Springer, Berlin, 1994. 10.1007/978-3-642-57916-5Suche in Google Scholar
[28] G. Pourcin, Deformations of coherent foliations on a compact normal space, Ann. Inst. Fourier (Grenoble) 37 (1987), no. 2, 33–48. 10.5802/aif.1085Suche in Google Scholar
[29]
G. Pourcin,
Deformations of singular holomorphic foliations on reduced compact
[30] F. Quallbrunn, Families of distributions and Pfaff systems under duality, J. Singul. 11 (2015), 164–189. 10.5427/jsing.2015.11gSuche in Google Scholar
[31] J. Vásquez Aquino, Cohomología del cociente GIT de cuárticas planas, Ph.D. Thesis, CIMAT, Guanajuato, 2022. Suche in Google Scholar
© 2024 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Rational points on a class of cubic hypersurfaces
- On fractional inequalities on metric measure spaces with polar decomposition
- Quantitative weighted estimates for the multilinear pseudo-differential operators in function spaces
- The 𝐿𝑝 restriction bounds for Neumann data on surface
- Quasi-triangular, factorizable Leibniz bialgebras and relative Rota–Baxter operators
- Big pure projective modules over commutative noetherian rings: Comparison with the completion
- Any Sasakian structure is approximated by embeddings into spheres
- GIT quotient of holomorphic foliations on ℂℙ2 of degree 2 and quartic plane curves
- The stable category of monomorphisms between (Gorenstein) projective modules with applications
- Gradings and graded linear maps on algebras
- A note on conjugacy of supplements in soluble periodic linear groups
- Discrete Ω-results for the Riemann zeta function
- Is addition definable from multiplication and successor?
- Hausdorff dimension of removable sets for elliptic and canceling homogeneous differential operators in the class of bounded functions
- Statistics of ranks, determinants and characteristic polynomials of rational matrices
- Controllability and diffeomorphism groups on manifolds with boundary
Artikel in diesem Heft
- Frontmatter
- Rational points on a class of cubic hypersurfaces
- On fractional inequalities on metric measure spaces with polar decomposition
- Quantitative weighted estimates for the multilinear pseudo-differential operators in function spaces
- The 𝐿𝑝 restriction bounds for Neumann data on surface
- Quasi-triangular, factorizable Leibniz bialgebras and relative Rota–Baxter operators
- Big pure projective modules over commutative noetherian rings: Comparison with the completion
- Any Sasakian structure is approximated by embeddings into spheres
- GIT quotient of holomorphic foliations on ℂℙ2 of degree 2 and quartic plane curves
- The stable category of monomorphisms between (Gorenstein) projective modules with applications
- Gradings and graded linear maps on algebras
- A note on conjugacy of supplements in soluble periodic linear groups
- Discrete Ω-results for the Riemann zeta function
- Is addition definable from multiplication and successor?
- Hausdorff dimension of removable sets for elliptic and canceling homogeneous differential operators in the class of bounded functions
- Statistics of ranks, determinants and characteristic polynomials of rational matrices
- Controllability and diffeomorphism groups on manifolds with boundary