A171109 -id:A171109 - cp's OEIS frontend

A171110 Gromov-Witten invariants for genus 2.

0, 0, 0, 27, 36855, 58444767, 122824720116

Offset: 1

N. J. A. Sloane, Sep 27 2010

a(8)-a(10) are conjectured to be 346860150644700, 1301798459308709880, 6383405726993645784000 [see Belorousski & Pandharipande and Eguchi & Xeong]. - Andrey Zabolotskiy, May 03 2022

Pasha Belorousski and Rahul Pandharipande, A descendent relation in genus 2, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 29 (2000), 171-191; arXiv:math/9803072 [math.AG], 1998.
Tohru Eguchi and Chuan-Sheng Xiong, Quantum Cohomology at Higher Genus: Topological Recursion Relations and Virasoro Conditions, Adv. Theor. Math. Phys., 2 (1998), 219-229; arXiv:hep-th/9801010, 1998.
Sergey Fomin and Grigory Mikhalkin, Labeled floor diagrams for plane curves, Journal of the European Mathematical Society 012.6 (2010): 1453-1496; arXiv:0906.3828 [math.AG], 2009-2010.
Andreas Gathmann, Topological recursion relations and Gromov-Witten invariants in higher genus, arXiv:math/0305361 [math.AG], 2003.

Cf. A171109.

a(7) from Gathmann added by Andrey Zabolotskiy, May 02 2022

A171111 Gromov-Witten invariants for genus 3.

Original entry on oeis.org

0, 0, 0, 1, 7915, 34435125, 153796445095

Offset: 1

N. J. A. Sloane, Sep 27 2010

a(8)-a(10) are conjectured to be 800457740515775, 5039930694167991360, 38747510483053595091600 [see Eguchi & Xeong]. - Andrey Zabolotskiy, May 03 2022

Tohru Eguchi and Chuan-Sheng Xiong, Quantum Cohomology at Higher Genus: Topological Recursion Relations and Virasoro Conditions, Adv. Theor. Math. Phys., 2 (1998), 219-229; arXiv:hep-th/9801010, 1998.
Sergey Fomin and Grigory Mikhalkin, Labeled floor diagrams for plane curves, Journal of the European Mathematical Society 012.6 (2010): 1453-1496; arXiv:0906.3828 [math.AG], 2009-2010.
Andreas Gathmann, Topological recursion relations and Gromov-Witten invariants in higher genus, arXiv:math/0305361 [math.AG], 2003.

Cf. A171109.

a(7) from Gathmann added by Andrey Zabolotskiy, May 02 2022

A171105 Multicomponent Gromov-Witten invariants for genus 0.

Original entry on oeis.org

1, 1, 12, 675, 109781, 40047888

Offset: 1

N. J. A. Sloane, Sep 27 2010

In this entry and in A171104, a multicomponent Gromov-Witten invariant is the number of (possibly reducible, hence "multicomponent") curves in CP^2 of degree n and genus g passing through given 3n-1+g points, so this is the Severi degree N(n, delta) where cogenus delta = (n-1)*(n-2)/2 - g, cf. A171108 and references therein. In particular, a(5) = A171116(5). - Andrey Zabolotskiy, May 04 2022

Florian Block, Computing node polynomials for plane curves, arXiv:1006.0218 [math.AG], 2010-2011; Math. Res. Lett. 18, (2011), no. 4, 621-643. See Appendix B.
Grigory Mikhalkin, Enumerative tropical algebraic geometry in R^2, arXiv:math/0312530 [math.AG], 2003-2004.

Cf. A171104, A171108, A171116.

Cf. Gromov-Witten invariants, counting irreducible curves only: A171109, A171110, A171111.

a(5)-a(6) added by Andrey Zabolotskiy, May 04 2022

cp's OEIS Frontend

A171110 Gromov-Witten invariants for genus 2.

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A171111 Gromov-Witten invariants for genus 3.

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A171105 Multicomponent Gromov-Witten invariants for genus 0.

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