Relevant bibliographies by topics / Abelian surfaces

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Abelian surfaces'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Abelian surfaces"

1

Hulek, Klaus, and Steven H. Weintraub. "Bielliptic abelian surfaces." Mathematische Annalen 283, no. 3 (1989): 411–29. http://dx.doi.org/10.1007/bf01442737.

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Garbagnati, Alice. "On K3 Surface Quotients of K3 or Abelian Surfaces." Canadian Journal of Mathematics 69, no. 02 (2017): 338–72. http://dx.doi.org/10.4153/cjm-2015-058-1.

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Abstract The aim of this paper is to prove that a K3 surface is the minimal model of the quotient of an Abelian surface by a group G (respectively of a K3 surface by an Abelian group G) if and only if a certain lattice is primitively embedded in its Néron-Severi group. This allows one to describe the coarse moduli space of the K3 surfaces that are (rationally) G-covered by Abelian or K3 surfaces (in the latter case G is an Abelian group). When G has order 2 or G is cyclic and acts on an Abelian surface, this result is already known; we extend it to the other cases. Moreover, we prove that a K3
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3

Alfonso Bonfanti, Matteo, and Bert van Geemen. "Abelian Surfaces with an Automorphism and Quaternionic Multiplication." Canadian Journal of Mathematics 68, no. 1 (2016): 24–43. http://dx.doi.org/10.4153/cjm-2014-045-4.

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AbstractWe construct one-dimensional families of Abelian surfaces with quaternionic multiplication, which also have an automorphism of order three or four. Using Barth's description of the moduli space of (2,4)- polarized Abelian surfaces, we find the Shimura curve parametrizing these Abelian surfaces in a specific case. We explicitly relate these surfaces to the Jacobians of genus two curves studied by Hashimoto and Murabayashi. We also describe a (Humbert) surface in Barth's moduli space that parametrizes Abelian surfaces with real multiplication by .
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4

Calegari, Frank, Shiva Chidambaram, and Alexandru Ghitza. "Some modular abelian surfaces." Mathematics of Computation 89, no. 321 (2019): 387–94. http://dx.doi.org/10.1090/mcom/3434.

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Chepelev, Iouri. "Non-Abelian Wilson Surfaces." Journal of High Energy Physics 2002, no. 02 (2002): 013. http://dx.doi.org/10.1088/1126-6708/2002/02/013.

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Yoshihara, Hisao. "Quotients of abelian surfaces." Publications of the Research Institute for Mathematical Sciences 31, no. 1 (1995): 135–43. http://dx.doi.org/10.2977/prims/1195164795.

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7

González-Diez, G., G. A. Jones, and D. Torres-Teigell. "Beauville Surfaces with Abelian Beauville Group." MATHEMATICA SCANDINAVICA 114, no. 2 (2014): 191. http://dx.doi.org/10.7146/math.scand.a-17106.

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A Beauville surface is a rigid surface of general type arising as a quotient of a product of curves $C_{1}$, $C_{2}$ of genera $g_{1},g_{2}\ge 2$ by the free action of a finite group $G$. In this paper we study those Beauville surfaces for which $G$ is abelian (so that $G\cong \mathsf{Z}_{n}^{2}$ with $\gcd(n,6)=1$ by a result of Catanese). For each such $n$ we are able to describe all such surfaces, give a formula for the number of their isomorphism classes and identify their possible automorphism groups. This explicit description also allows us to observe that such surfaces are all defined o
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8

Lesfari, A. "Abelian surfaces and Kowalewski's top." Annales scientifiques de l'École normale supérieure 21, no. 2 (1988): 193–223. http://dx.doi.org/10.24033/asens.1556.

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9

Silverberg, A., and Yu G. Zarhin. "Inertia groups and abelian surfaces." Journal of Number Theory 110, no. 1 (2005): 178–98. http://dx.doi.org/10.1016/j.jnt.2004.05.015.

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10

Birkenhake, C., H. Lange, and D. van Straten. "Abelian surfaces of type (1,4)." Mathematische Annalen 285, no. 4 (1989): 625–46. http://dx.doi.org/10.1007/bf01452051.

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Dissertations / Theses on the topic "Abelian surfaces"

1

Marini, A. "On the degenerations of (1,7)-polarised abelian surfaces." Thesis, University of Bath, 2002. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.394153.

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2

Rose, Simon Charles Florian. "Counting hyperelliptic curves in Abelian surfaces with quasi-modular forms." Thesis, University of British Columbia, 2012. http://hdl.handle.net/2429/42091.

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In this thesis we produce a generating function for the number of hyperelliptic curves (up to translation) on a polarized Abelian surface using the crepant resolution conjecture and the Yau-Zaslow formula. We present a formula to compute these in terms of P. A. MacMahon's generalized sum-of-divisors functions, and prove that they are quasi-modular forms.
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3

Manoharmayum, Jayanta. "Mod n representations arising from elliptic curves and abelian surfaces." Thesis, University of Cambridge, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.624411.

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Alagal, Wafa Abdullah. "Application of Bridgeland stability to the geometry of abelian surfaces." Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/20440.

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A key property of projective varieties is the very ampleness of line bundles as this provides embeddings into projective space and allows us to express the variety in equational terms. In this thesis we study the general version of this property which is k- very ampleness of line bundles. We introduce the notation of critical k-very ampleness and compute it for abelian surfaces. The property of k-very ampleness is usually discussed using tools from divisor theory but we take a different approach and use methods from derived algebraic geometry as part of program to use properties of the derived
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Kazaz, Mustafa. "Finite groups and coverings of surfaces." Thesis, University of Southampton, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.264739.

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Sumi, Ken. "Tropical Theta Functions and Riemann-Roch Inequality for Tropical Abelian Surfaces." Doctoral thesis, Kyoto University, 2021. http://hdl.handle.net/2433/263432.

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7

Biroth, Laura [Verfasser]. "Integrable systems and a moduli space for (1,6)-polarised abelian surfaces / Laura Biroth." Mainz : Universitätsbibliothek Mainz, 2019. http://d-nb.info/1200661478/34.

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Cesarano, Luca [Verfasser], and Fabrizio [Akademischer Betreuer] Catanese. "Canonical Surfaces and Hypersurfaces in in Abelian Varieties / Luca Cesarano ; Betreuer: Fabrizio Catanese." Bayreuth : Universität Bayreuth, 2018. http://d-nb.info/1160301913/34.

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9

Gillibert, Florence. "Surfaces abéliennes à multiplication quaternionique et points rationnels de quotients d'Atkin-Lehner de courbes de Shimura." Thesis, Bordeaux 1, 2011. http://www.theses.fr/2011BOR14374/document.

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Dans cette thèse nous étudions deux problèmes. Le premier est la non-existence de pointsrationnels non spéciaux sur des quotients d’Atkin-Lehner de courbes de Shimura. Le se-cond est l’absence de surfaces abéliennes rationnelles à multiplication potentiellementquaternioniques munies d’une structure de niveau. Ces deux problèmes sont liés car unesurface abélienne rationnelle simple à multiplication potentiellement quaternionique cor-respond à un point rationnel non spécial sur un certain quotient d’Atkin-Lehner de courbede Shimura.Dans une première partie nous expliquons comment vérifier un cri
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Keil, Stefan. "On non-square order Tate-Shafarevich groups of non-simple abelian surfaces over the rationals." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2014. http://dx.doi.org/10.18452/16901.

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Bei elliptischen Kurven E/K über einem Zahlkörper K zwingt die Cassels-Tate Paarung die Ordnung der Tate-Shafarevich Gruppe Sha(E/K) zu einem Quadrat. Ist A/K eine prinzipal polarisierte abelschen Varietät, so ist bewiesen, daß die Ordnung von Sha(A/K) ein Quadrat oder zweimal ein Quadrat ist. William Stein vermutet, daß es für jede quadratfreie positive ganze Zahl k eine abelsche Varietät A/Q gibt, mit #Sha(A/Q)=kn². Jedoch ist es ein offenes Problem was zu erwarten ist, wenn die Dimension von A/Q beschränkt wird. Betrachtet man ausschließlich abelsche Flächen B/Q, so liefern Resultate von
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Books on the topic "Abelian surfaces"

1

H, Lange. Complex Abelian varieties. Springer-Verlag, 1992.

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2

1943-, Lange H., and Lange H. 1943-, eds. Complex Abelian varieties. 2nd ed. Springer, 2004.

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3

Lange, Herbert. Complex Abelian varieties. Springer, 1992.

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4

Faltings, Gerd. Degeneration of Abelian varieties. Springer-Verlag, 1990.

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5

Muñoz Porras, José M., Sorin Popescu, and Rubí E. Rodríguez, eds. The Geometry of Riemann Surfaces and Abelian Varieties. American Mathematical Society, 2006. http://dx.doi.org/10.1090/conm/397.

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6

Hulek, Klaus. Moduli spaces of Abelian surfaces: Compactification, degenerations, and theta functions. Walter de Gruyter, 1993.

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Muñoz Porras, Jose M. 1956-, Popescu Sorin 1963-, Rodríguez Rubí E. 1953-, and Recillas-Pishmish Sevín 1943-, eds. The geometery [sic] of Riemann surfaces and Abelian varieties: III Iberoamerican Congress on Geometry in honor of Professor Sevin Recillas-Pishmish's 60th birthday, June 8-12, 2004, Salamanca, Spain. American Mathematical Society, 2006.

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Complex analysis 2: Riemann surfaces, several complex variables, abelian functions, higher modular functions. Springer, 2011.

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9

Hironaka, Eriko. Abelian coverings of the complex projective plane branched along configurations of real lines. American Mathematical Society, 1993.

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Rodríguez, Rubí E., 1953- editor of compilation, ed. Riemann and Klein surfaces, automorphisms, symmetries and moduli spaces: Conference in honor of Emilio Bujalance on Riemann and Klein surfaces, symmetries and moduli spaces, June 24-28, 2013, Linköping University, Linköping, Sweden. American Mathematical Society, 2014.

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Book chapters on the topic "Abelian surfaces"

1

Lange, Herbert, and Christina Birkenhake. "Abelian Surfaces." In Complex Abelian Varieties. Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-662-02788-2_12.

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Birkenhake, Christina, and Herbert Lange. "Abelian Surfaces." In Complex Abelian Varieties. Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-06307-1_12.

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Voight, John. "QM abelian surfaces." In Graduate Texts in Mathematics. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-56694-4_43.

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Howard, Benjamin, and Tonghai Yang. "Moduli Spaces of Abelian Surfaces." In Intersections of Hirzebruch–Zagier Divisors and CM Cycles. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-23979-3_3.

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Geer, Gerard. "Moduli of Abelian Schemes with Real Multiplication." In Hilbert Modular Surfaces. Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/978-3-642-61553-5_12.

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Van der Geer, G., and T. Katsura. "Formal Brauer Groups and Moduli of Abelian Surfaces." In Moduli of Abelian Varieties. Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8303-0_6.

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Edixhoven, Bas. "On the André-Oort Conjecture for Hilbert Modular Surfaces." In Moduli of Abelian Varieties. Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8303-0_4.

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Kresch, Andrew, and Yuri Tschinkel. "Integral Points on Punctured Abelian Surfaces." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/3-540-45455-1_16.

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Harder, Günter. "Compact Riemann surfaces and Abelian Varieties." In Aspects of Mathematics. Springer Fachmedien Wiesbaden, 2011. http://dx.doi.org/10.1007/978-3-8348-8330-8_5.

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Ogus, Arthur. "Singularities of the Height Strata in the Moduli of K3 Surfaces." In Moduli of Abelian Varieties. Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8303-0_12.

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Conference papers on the topic "Abelian surfaces"

1

Korzec, Tomasz, and Ulli Wolff. "Simulating the Random Surface representation of Abelian Gauge Theories." In 31st International Symposium on Lattice Field Theory LATTICE 2013. Sissa Medialab, 2014. http://dx.doi.org/10.22323/1.187.0038.

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