Advanced search
Publication Cover
Communications in Algebra Volume 48, 2020 - Issue 1
Submit an article Journal homepage
47
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Reconstruction of singularities on orbifold del Pezzo surfaces from their Hilbert series

Ben WormleightonDepartment of Mathematics, University of California at Berkeley, Berkeley, CA, USACorrespondence[email protected]
ORCID Iconhttp://orcid.org/0000-0003-0759-7826View further author information
ORCID Icon
Pages 119-140 | Received 29 Apr 2019, Accepted 01 Jun 2019, Published online: 09 Jul 2019

References

  • Akhtar, M., Coates, T., Corti, A., Heuberger, L., Kasprzyk, A., Oneto, A., Petracci, A., Prince, T., Tveiten, K. (2015). Mirror symmetry and the classification of orbifold del Pezzo surfaces. Proc. Amer. Math. Soc. 144(2):513–527. DOI:10.1090/proc/12876.
  • Akhtar, M., Coates, T., Galkin, S., Kasprzyk, A. M. (2012). Minkowski polynomials and mutations. Sigma 8:094. arXiv:1212:1785.
  • Akhtar, M., Kasprzyk, A. (2014). Singularity content. arXiv. Preprint. arXiv:1401:5458.
  • Akhtar, M. E., Kasprzyk, A. M. (2016). Mutations of fake weighted projective planes. Proc. Edinb. Math. Soc. 59(2):271–285. DOI:10.1017/S0013091515000115.
  • Bass, H. (1963). On the ubiquity of Gorenstein rings. Math. Z. 82(1):8–28. DOI:10.1007/BF01112819.
  • Beck, M., Robins, S. (2004). Dedekind Sums: A Combinatorial-Geometric Viewpoint, Vol. 64. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pp. 25–36.
  • Buckley, A., Reid, M., Zhou, S. (2013). Ice cream and orbifold Riemann-Roch. Izv. Math. 77(3):461. DOI:10.1070/IM2013v077n03ABEH002644.
  • Coates, T., Corti, A., Galkin, S., Golyshev, V., Kasprzyk, A. (2012). Mirror symmetry and Fano manifolds. arXiv. Preprint. arXiv1212:1722.
  • Cox, D. A., Little, J. B., Schenck, H. K. (2011). Toric Varieties. Providence, RI: American Mathematical Society.
  • Kollár, J., Shepherd-Barron, N. I. (1988). Threefolds and deformations of surface singularities. Invent. Math. 91(2):299–338. DOI:10.1007/BF01389370.
  • Kasprzyk, A. M., Wormleighton, B. (2018). Quasi-period collapse for duals to Fano polygons: an explanation arising from algebraic geometry. arXiv. Preprint. arXiv:1810.12472.
  • Hacking, P., Prokhorov, Y. (2010). Smoothable del Pezzo surfaces with quotient singularities. Compos. Math. 146(1):169–192. DOI:10.1112/S0010437X09004370
  • Migliore, J. C., Nagel, U., Zanello, F. (2008). A characterization of Gorenstein Hilbert functions in codimension four with small initial degree. Math. Res. Lett. 15:331–349.
  • Pommersheim, J. E. (1993). Toric varieties, lattice points and Dedekind sums. Math. Ann. 295(1):1–24. DOI:10.1007/BF01444874.
  • Reid, M. (1985). Young person’s guide to canonical singularities. Algebraic Geometry, Bowdoin. Proceedings of Symposia in Pure Mathematics, Vol. 46. Providence, RI: American Mathematical Society, pp. 345–414.
  • Zagier, D. (1973). Higher dimensional Dedekind sums. Math. Ann. 202(2):149–172. DOI:10.1007/BF01351173.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.