Tangency quantum cohomology and characteristic numbers

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

Tangency quantum cohomology and characteristic numbers. / Kock, Joachim.

In: Anais da Academia Brasileira de Ciencias, Vol. 73, No. 3, 09.2001, p. 319-326.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Kock, J 2001, 'Tangency quantum cohomology and characteristic numbers', Anais da Academia Brasileira de Ciencias, vol. 73, no. 3, pp. 319-326. https://doi.org/10.1590/S0001-37652001000300002

APA

Kock, J. (2001). Tangency quantum cohomology and characteristic numbers. Anais da Academia Brasileira de Ciencias, 73(3), 319-326. https://doi.org/10.1590/S0001-37652001000300002

Vancouver

Kock J. Tangency quantum cohomology and characteristic numbers. Anais da Academia Brasileira de Ciencias. 2001 Sep;73(3):319-326. https://doi.org/10.1590/S0001-37652001000300002

Author

Kock, Joachim. / Tangency quantum cohomology and characteristic numbers. In: Anais da Academia Brasileira de Ciencias. 2001 ; Vol. 73, No. 3. pp. 319-326.

Bibtex

@article{290497f4a0834424a755cca301ddba24,
title = "Tangency quantum cohomology and characteristic numbers",
abstract = "This work establishes a connection between gravitational quantum cohomology and enumerative geometry of rational curves (in a projective homogeneous variety) subject to conditions of infinitesimal nature like, for example, tangency. The key concept is that of modified psi classes, which are well suited for enumerative purposes and substitute the tautological psi classes of 2D gravity. The main results are two systems of differential equations for the generating function of certain top products of such classes. One is topological recursion while the other is Witten-Dijkgraaf-Verlinde-Verlinde. In both cases, however, the background metric is not the usual Poincare metric but a certain deformation of it, which surprisingly encodes all the combinatorics of the peculiar way modified psi classes restrict to the boundary. This machinery is applied to various enumerative problems, among which characteristic numbers in any projective homogeneous variety, characteristic numbers for curves with cusp, prescribed triple contact, or double points.",
keywords = "enumerative geometry, characteristic numbers, quantum cohomology, Gromov-Witten invariants, ENUMERATIVE GEOMETRY",
author = "Joachim Kock",
year = "2001",
month = sep,
doi = "10.1590/S0001-37652001000300002",
language = "English",
volume = "73",
pages = "319--326",
journal = "Anais da Academia Brasileira de Ciencias.",
issn = "0001-3765",
publisher = "Academia Brasileira de Ci{\^e}ncias",
number = "3",

}

RIS

TY - JOUR

T1 - Tangency quantum cohomology and characteristic numbers

AU - Kock, Joachim

PY - 2001/9

Y1 - 2001/9

N2 - This work establishes a connection between gravitational quantum cohomology and enumerative geometry of rational curves (in a projective homogeneous variety) subject to conditions of infinitesimal nature like, for example, tangency. The key concept is that of modified psi classes, which are well suited for enumerative purposes and substitute the tautological psi classes of 2D gravity. The main results are two systems of differential equations for the generating function of certain top products of such classes. One is topological recursion while the other is Witten-Dijkgraaf-Verlinde-Verlinde. In both cases, however, the background metric is not the usual Poincare metric but a certain deformation of it, which surprisingly encodes all the combinatorics of the peculiar way modified psi classes restrict to the boundary. This machinery is applied to various enumerative problems, among which characteristic numbers in any projective homogeneous variety, characteristic numbers for curves with cusp, prescribed triple contact, or double points.

AB - This work establishes a connection between gravitational quantum cohomology and enumerative geometry of rational curves (in a projective homogeneous variety) subject to conditions of infinitesimal nature like, for example, tangency. The key concept is that of modified psi classes, which are well suited for enumerative purposes and substitute the tautological psi classes of 2D gravity. The main results are two systems of differential equations for the generating function of certain top products of such classes. One is topological recursion while the other is Witten-Dijkgraaf-Verlinde-Verlinde. In both cases, however, the background metric is not the usual Poincare metric but a certain deformation of it, which surprisingly encodes all the combinatorics of the peculiar way modified psi classes restrict to the boundary. This machinery is applied to various enumerative problems, among which characteristic numbers in any projective homogeneous variety, characteristic numbers for curves with cusp, prescribed triple contact, or double points.

KW - enumerative geometry

KW - characteristic numbers

KW - quantum cohomology

KW - Gromov-Witten invariants

KW - ENUMERATIVE GEOMETRY

U2 - 10.1590/S0001-37652001000300002

DO - 10.1590/S0001-37652001000300002

M3 - Journal article

VL - 73

SP - 319

EP - 326

JO - Anais da Academia Brasileira de Ciencias.

JF - Anais da Academia Brasileira de Ciencias.

SN - 0001-3765

IS - 3

ER -

ID: 331504963