---
title: "Bibliography"
canonical: "https://docs.magma-maths.org/AlgebraicGeometry/AlgebraicSurfaces/bibliography.html"
source: "https://docs.magma-maths.org/AlgebraicGeometry/AlgebraicSurfaces/bibliography.md"
part: "Algebraic Geometry"
chapter: "Algebraic Surfaces"
breadcrumbs:
  - {"title": "Magma Handbook", "source": "../../index.md"}
  - {"title": "Algebraic Geometry", "source": "../index-algebraic-geometry.md"}
  - {"title": "Algebraic Surfaces", "source": "index-algebraic-surfaces.md"}
prev: {"title": "Degree $2$ K3 Surfaces", "source": "deg-2-K3-srfcs.md"}
next: {"title": "Riemann Surfaces", "source": "../RiemannSurfaces/index-riemann-surfaces.md"}
---

# Bibliography

<a id="cite-bhpv-04"></a>
- **[BHPdV04]** Barth, Hulek, Peters, and Van de Ven. *Compact Complex Surfaces*. Ergebnisse der Mathematik und ihrer Grenzgebiete 4. Springer, second edition, 2004. ISBN 3-540-00832-2.
<a id="cite-tb2007"></a>
- **[Bec07]** Tobias Beck. Formal Desingularization of Surfaces – The Jung Method Revisited –. Technical Report 2007-31, RICAM, December 2007. http://www.ricam.oeaw.ac.at/publications/reports/.
<a id="cite-tb2008"></a>
- **[Bec08]** Tobias Beck. Software Documentation. Technical Report 2008-8, RICAM, May 2008. http://www.ricam.oeaw.ac.at/publications/reports/.
<a id="cite-tb2007b"></a>
- **[BS08]** Tobias Beck and Josef Schicho. Adjoint Computation for Hypersurfaces Using Formal Desingularizations. Technical Report 2008-2, RICAM, January 2008. http://www.ricam.oeaw.ac.at/publications/reports/.
<a id="cite-bfhn19"></a>
- **[BFHN]** M. Besier, D. Festi, M.C. Harrison, and B. Naskrecki. Arithmetic and geometry of a K3 surface emerging from virtual corrections to Drell-Yan scattering. preprint arXiv:1908.01079 [math.AG].
<a id="cite-dp-deg8"></a>
- **[dGP]** W.A. de Graaf and J. Pilnikova. Parametrizing Del Pezzo surfaces of degree 8 using Lie algebras. http://arxiv.org/abs/math.NT/0512477.
<a id="cite-dp-deg9"></a>
- **[dG06]** W. de Graaf, M. Harrison, J. Pilnikova and J. Schicho. A Lie Algebra Method for Rational Parametrization of Severi-Brauer Surfaces. *J. Alg.*, 303(2):514–529, 2006.
<a id="cite-decker-ein-schreyer-93"></a>
- **[DES93]** Decker, Ein, and Schreyer. Construction of surfaces in P4. *J. Algebraic Geometry*, 2:185–237, 1993.
<a id="cite-eis05"></a>
- **[Eis05]** David Eisenbud. *The geometry of syzygies: a second course in commutative algebra and algebraic geometry*. Volume 225 of Graduate Texts in Mathematics. Springer, New York–Berlin–Heidelberg, 2005.
<a id="cite-elsenhans-good-models"></a>
- **[Els]** Andreas-Stephan Elsenhans. Good models for cubic surfaces. (To appear). URL: [http://www.staff.uni-bayreuth.de/ btm216/](http://www.staff.uni-bayreuth.de/ btm216/).
<a id="cite-elsenhans-jahnel-double-six"></a>
- **[EJ10a]** Andreas-Stephan Elsenhans and Jörg Jahnel. Cubic surfaces with a Galois invariant double-six. *Cent. Eur. J. Math.*, 8(4):646–661, 2010.
<a id="cite-dfpiclatt18"></a>
- **[Fes]** Dino Festi. A practical algorithm to compute the geometric picard lattices of K3 surfaces of degree 2. preprint arXiv:1808.00351 [math.AG].
<a id="cite-dp-deg5"></a>
- **[GSHPBS12]** J. Gonzalez-Sanchez, M. Harrison, I. Polo-Blanco, J. Schicho. “Algorithms For Del Pezzo Surfaces of Degree 5 (Construction, Parametrization).” JSC, 147(3), 342–353. 2012.
<a id="cite-dp-deg6"></a>
- **[HS06]** M.C. Harrison and J. Schicho. Rational Parametrisation for Degree 6 Del Pezzo Surfaces using Lie Algebras. In *Proceedings ISSAC'06*. 2006.
<a id="cite-hartshorne"></a>
- **[Har77]** Robin Hartshorne. *Algebraic Geometry, GTM 52*. Springer, ASpringer, 1977.
<a id="cite-hor2-76"></a>
- **[Hor76]** E. Horikawa. Algebraic Surfaces of General Type with Small $c_1^2$. II. *Invent. Math.*, 37:121–155, 1976.
<a id="cite-mr1438547"></a>
- **[Hun96]** Bruce Hunt. *The geometry of some special arithmetic quotients*. Volume 1637 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, 1996.
<a id="cite-man-cub-forms"></a>
- **[Man86]** Yu. I. Manin. *Cubic Forms (2nd ed.)*. North-Holland Publishing Co., Amsterdam, 1986. Vol. 4 of North-Holland Mathematical Library.
<a id="cite-mr1780430"></a>
- **[RS00]** Kristian Ranestad and Frank-Olaf Schreyer. Varieties of sums of powers. *J. Reine Angew. Math.*, 525:147–181, 2000. URL: [http://dx.doi.org/10.1515/crll.2000.064](http://dx.doi.org/10.1515/crll.2000.064), [doi:10.1515/crll.2000.064](https://doi.org/10.1515/crll.2000.064).
<a id="cite-std73"></a>
- **[SD74]** Bernard Saint-Donat. Projective Models of K-3 Surfaces. *Am. Jour. Math.*, 96(4):602–639, 1974.
<a id="cite-mr0094753"></a>
- **[Sal58]** George Salmon. *A treatise on the analytic geometry of three dimensions*. Revised by R. A. P. Rogers. 7th ed. Vol. 1. Edited by C. H. Rowe. Chelsea Publishing Company, New York, 1958.
<a id="cite-js1998b"></a>
- **[Sch98]** Josef Schicho. Rational parametrization of surfaces. *J. Symbolic Comput.*, 26(1):1–29, 1998.
<a id="cite-js2000"></a>
- **[Sch00a]** Josef Schicho. Proper parametrization of surfaces with a rational pencil. In *Proceedings of the 2000 International Symposium on Symbolic and Algebraic Computation (St. Andrews)*, 292–300 (electronic). New York, 2000. ACM.
<a id="cite-somm-ven-adj-map"></a>
- **[SvdV87]** A.J. Sommese and A. van der Ven. On the adjunction mapping. *Math. Ann.*, 278:593–603, 1987.