Rocky Mountain Journal of Mathematics

Psi-class intersections on Hassett spaces for genus 0 with all weights $\frac {1}{2}$

Nand Sharma

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Abstract

Hassett spaces are moduli spaces of weighted stable pointed curves. We consider such spaces of curves of genus $0$ with weights all $\frac {1}{2}$. These spaces are interesting, since they are isomorphic to $\overline{M}_{0,n}$ but have different universal families and different intersection theory. We develop a closed formula for intersections of $\psi $-classes on such spaces. In our main result, we encode the formula for top intersections in a generating function obtained by applying a differential operator to the Witten potential.

Article information

Source
Rocky Mountain J. Math., Volume 49, Number 7 (2019), 2297-2324.

Dates
First available in Project Euclid: 8 December 2019

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1575774139

Digital Object Identifier
doi:10.1216/RMJ-2019-49-7-2297

Mathematical Reviews number (MathSciNet)
MR4039971

Subjects
Primary: 14Q99: None of the above, but in this section

Keywords
$\psi $ classes Hassett spaces

Citation

Sharma, Nand. Psi-class intersections on Hassett spaces for genus 0 with all weights $\frac {1}{2}$. Rocky Mountain J. Math. 49 (2019), no. 7, 2297--2324. doi:10.1216/RMJ-2019-49-7-2297. https://projecteuclid.org/euclid.rmjm/1575774139


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References

  • V. Alexeev and G.M. Guy, Moduli of weighted stable maps and their gravitational descendants, J. Inst. Math. Jussieu 7 (2008), no. 3, 425–456. @articlealexeev_guy_2008, MRKEY = MR2427420, AUTHOR = Alexeev, Valery and Guy, G. Michael, TITLE = Moduli of weighted stable maps and their gravitational descendants, JOURNAL = J. Inst. Math. Jussieu, FJOURNAL = Journal of the Institute of Mathematics of Jussieu. JIMJ. Journal de l'Institut de Mathématiques de Jussieu, VOLUME = 7, YEAR = 2008, NUMBER = 3, PAGES = 425–456, ISSN = 1474-7480, MRCLASS = 14N35 (14D20), MRNUMBER = 2427420, MRREVIEWER = Hsian-Hua Tseng, DOI = 10.1017/S1474748008000108, URL =,
  • D. Ayala and R. Cavalieri, Counting bitangents with stable maps, Expo. Math. 24 (2006), no. 4, 307–335. @articleAYALA2006307, MRKEY = MR2313122, AUTHOR = Ayala, David and Cavalieri, Renzo, TITLE = Counting bitangents with stable maps, JOURNAL = Expo. Math., FJOURNAL = Expositiones Mathematicae, VOLUME = 24, YEAR = 2006, NUMBER = 4, PAGES = 307–335, ISSN = 0723-0869, MRCLASS = 14N10 (14N35), MRNUMBER = 2313122, MRREVIEWER = Artur Elezi, DOI = 10.1016/j.exmath.2006.01.003, URL =,
  • A. Bayer and Y.I. Manin, Stability conditions, wall-crossing and weighted Gromov–Witten invariants, Mosc. Math. J. 9 (2006), no. 1, 3–32. @articleweightedGW, MRKEY = MR2567394, AUTHOR = Bayer, Arend and Manin, Yu. I., TITLE = Stability conditions, wall-crossing and weighted Gromov-Witten invariants, JOURNAL = Mosc. Math. J., FJOURNAL = Moscow Mathematical Journal, VOLUME = 9, YEAR = 2009, NUMBER = 1, PAGES = 3–32, backmatter, ISSN = 1609-3321, MRCLASS = 14N35 (14D23 14H10 53D45), MRNUMBER = 2567394, MRREVIEWER = Yunfeng Jiang, DOI = 10.17323/1609-4514-2009-9-1-3-32, URL =,
  • R. Cavalieri, Moduli spaces of pointed rational curves, lecture notes (2016). http://www.math.colostate.edu/~ renzo/teaching/Moduli16/Fields.pdf
  • P. Deligne and D. Mumford, The irreducibility of the space of curves of given genus, Inst. Hautes Études Sci. Publ. Math. 36 (1969), 75–109. @articleDeligne, MRKEY = MR0262240, AUTHOR = Deligne, P. and Mumford, D., TITLE = The irreducibility of the space of curves of given genus, JOURNAL = Inst. Hautes Études Sci. Publ. Math., FJOURNAL = Institut des Hautes Études Scientifiques. Publications Mathématiques, NUMBER = 36, YEAR = 1969, PAGES = 75–109, ISSN = 0073-8301, MRCLASS = 14.20, MRNUMBER = 0262240, MRREVIEWER = Manfred Herrmann, URL = http://www.numdam.org/item?id=PMIHES_1969__36__75_0,
  • J. Harris and I. Morrison, Moduli of curves, Graduate Texts in Mathematics 187, Springer (1998). @bookmod, MRKEY = MR1631825, AUTHOR = Harris, Joe and Morrison, Ian, TITLE = Moduli of curves, SERIES = Graduate Texts in Mathematics, VOLUME = 187, PUBLISHER = Springer-Verlag, New York, YEAR = 1998, PAGES = xiv+366, ISBN = 0-387-98438-0; 0-387-98429-1, MRCLASS = 14H10 (14-02 14D20 14D22), MRNUMBER = 1631825, MRREVIEWER = R. F. Lax,
  • B. Hassett, Moduli spaces of weighted pointed stable curves, Adv. Math. 173 (2003), no. 2, 316–352. @articleHASSETT2003316, MRKEY = MR1957831, AUTHOR = Hassett, Brendan, TITLE = Moduli spaces of weighted pointed stable curves, JOURNAL = Adv. Math., FJOURNAL = Advances in Mathematics, VOLUME = 173, YEAR = 2003, NUMBER = 2, PAGES = 316–352, ISSN = 0001-8708, MRCLASS = 14H10 (14D22 14E30), MRNUMBER = 1957831, MRREVIEWER = Ivan S. Kausz, DOI = 10.1016/S0001-8708(02)00058-0, URL =,
  • J. Kock, Notes on psi classes, lecture notes (2001). http://mat.uab.es/~ kock/ GW/notes/psi-notes.pdf
  • J. Kock and I. Vainsencher, An invitation to quantum cohomology: Kontsevich's formula for rational plane curves, Progress in Mathematics 249, Birkhäuser (2007). @bookinvitation, MRKEY = MR2262630, AUTHOR = Kock, Joachim and Vainsencher, Israel, TITLE = An invitation to quantum cohomology, SERIES = Progress in Mathematics, VOLUME = 249, NOTE = Kontsevich's formula for rational plane curves, PUBLISHER = Birkhäuser Boston, Inc., Boston, MA, YEAR = 2007, PAGES = xiv+159, ISBN = 978-0-8176-4456-7; 0-8176-4456-3, MRCLASS = 14N35 (14H15 14N10 53D45), MRNUMBER = 2262630, MRREVIEWER = Gary P. Kennedy,
  • A. Losev and Y. Manin, New moduli spaces of pointed curves and pencils of flat connections, Michigan Math. J. 48 (2000), no. 1, 443–472. @incollectionlosev2000, MRKEY = MR1786500, AUTHOR = Losev, A. and Manin, Y., TITLE = New moduli spaces of pointed curves and pencils of flat connections, NOTE = Dedicated to William Fulton on the occasion of his 60th birthday, JOURNAL = Michigan Math. J., FJOURNAL = Michigan Mathematical Journal, VOLUME = 48, YEAR = 2000, PAGES = 443–472, ISSN = 0026-2285, MRCLASS = 14N35 (14H10 53D45), MRNUMBER = 1786500, MRREVIEWER = Andrew Kresch, DOI = 10.1307/mmj/1030132728, URL =,