Descendant invariants and characteristic numbers

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Descendant invariants and characteristic numbers. / Graber, T; Kock, Joachim; Pandharipande, R.

In: American Journal of Mathematics, Vol. 124, No. 3, 06.2002, p. 611-647.

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

Harvard

Graber, T, Kock, J & Pandharipande, R 2002, 'Descendant invariants and characteristic numbers', American Journal of Mathematics, vol. 124, no. 3, pp. 611-647. https://doi.org/10.1353/ajm.2002.0014

APA

Graber, T., Kock, J., & Pandharipande, R. (2002). Descendant invariants and characteristic numbers. American Journal of Mathematics, 124(3), 611-647. https://doi.org/10.1353/ajm.2002.0014

Vancouver

Graber T, Kock J, Pandharipande R. Descendant invariants and characteristic numbers. American Journal of Mathematics. 2002 Jun;124(3):611-647. https://doi.org/10.1353/ajm.2002.0014

Author

Graber, T ; Kock, Joachim ; Pandharipande, R. / Descendant invariants and characteristic numbers. In: American Journal of Mathematics. 2002 ; Vol. 124, No. 3. pp. 611-647.

Bibtex

@article{1e5c401a815145798d3f1e60459fc0c8,
title = "Descendant invariants and characteristic numbers",
abstract = "On a stack of stable maps, the cotangent line classes are modified by subtracting certain boundary divisors. These modified cotangent line classes are compatible with forgetful morphisms, and are well-suited to enumerative geometry: tangency conditions allow simple expressions in terms of modified cotangent line classes. Topological recursion relations ate established among their top products in genus 0, yielding effective recursions for characteristic numbers of rational curves in any projective homogeneous variety. In higher genus, the obtained numbers are only virtual, due to contributions from spurious components of the space of maps. For the projective plane, the necessary corrections are determined in genus 1 and 2 to give the characteristic numbers in these cases.",
keywords = "GROMOV-WITTEN-INVARIANTS, PLANE-CURVES, ENUMERATIVE GEOMETRY, QUANTUM COHOMOLOGY",
author = "T Graber and Joachim Kock and R Pandharipande",
year = "2002",
month = jun,
doi = "10.1353/ajm.2002.0014",
language = "English",
volume = "124",
pages = "611--647",
journal = "American Journal of Mathematics",
issn = "0002-9327",
publisher = "TheJohns Hopkins University Press",
number = "3",

}

RIS

TY - JOUR

T1 - Descendant invariants and characteristic numbers

AU - Graber, T

AU - Kock, Joachim

AU - Pandharipande, R

PY - 2002/6

Y1 - 2002/6

N2 - On a stack of stable maps, the cotangent line classes are modified by subtracting certain boundary divisors. These modified cotangent line classes are compatible with forgetful morphisms, and are well-suited to enumerative geometry: tangency conditions allow simple expressions in terms of modified cotangent line classes. Topological recursion relations ate established among their top products in genus 0, yielding effective recursions for characteristic numbers of rational curves in any projective homogeneous variety. In higher genus, the obtained numbers are only virtual, due to contributions from spurious components of the space of maps. For the projective plane, the necessary corrections are determined in genus 1 and 2 to give the characteristic numbers in these cases.

AB - On a stack of stable maps, the cotangent line classes are modified by subtracting certain boundary divisors. These modified cotangent line classes are compatible with forgetful morphisms, and are well-suited to enumerative geometry: tangency conditions allow simple expressions in terms of modified cotangent line classes. Topological recursion relations ate established among their top products in genus 0, yielding effective recursions for characteristic numbers of rational curves in any projective homogeneous variety. In higher genus, the obtained numbers are only virtual, due to contributions from spurious components of the space of maps. For the projective plane, the necessary corrections are determined in genus 1 and 2 to give the characteristic numbers in these cases.

KW - GROMOV-WITTEN-INVARIANTS

KW - PLANE-CURVES

KW - ENUMERATIVE GEOMETRY

KW - QUANTUM COHOMOLOGY

U2 - 10.1353/ajm.2002.0014

DO - 10.1353/ajm.2002.0014

M3 - Journal article

VL - 124

SP - 611

EP - 647

JO - American Journal of Mathematics

JF - American Journal of Mathematics

SN - 0002-9327

IS - 3

ER -

ID: 331504832