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Journal articles on the topic 'Abelian surfaces'

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Published: 4 June 2021
Last updated: 1 February 2022

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1

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

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2

Garbagnati, Alice. "On K3 Surface Quotients of K3 or Abelian Surfaces." Canadian Journal of Mathematics 69, no. 02 (April 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 surface XG is the minimal model of the quotient of an Abelian surface by a group G if and only if a certain configuration of rational curves is present on XG . Again, this result was known only in some special cases, in particular, if G has order 2 or 3.
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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 (February 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 (April 1, 2019): 387–94. http://dx.doi.org/10.1090/mcom/3434.

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5

Chepelev, Iouri. "Non-Abelian Wilson Surfaces." Journal of High Energy Physics 2002, no. 02 (February 12, 2002): 013. http://dx.doi.org/10.1088/1126-6708/2002/02/013.

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6

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 (May 6, 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 over $\mathsf{Q}$.
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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 (January 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 (December 1989): 625–46. http://dx.doi.org/10.1007/bf01452051.

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11

Jassim, S. A. "Finite abelian actions on surfaces." Glasgow Mathematical Journal 35, no. 2 (May 1993): 225–34. http://dx.doi.org/10.1017/s0017089500009782.

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Let G be a finite abelian group of rank m, M an oriented compact connected surface, and F(G, M) the set of all orientation preserving free G-actions on M. Two actions φ1, φ2εF(G, M) are equivalent if there exists an orientation preserving homeomorphism h of M such thathφ1(f) for all f ε G.
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12

Vinberg, Ernest. "On Abelian coverings of surfaces." Michigan Mathematical Journal 55, no. 3 (December 2007): 631–50. http://dx.doi.org/10.1307/mmj/1197056460.

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13

Ramanan, S. "Ample Divisors on Abelian Surfaces." Proceedings of the London Mathematical Society s3-51, no. 2 (September 1985): 231–45. http://dx.doi.org/10.1112/plms/s3-51.2.231.

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14

Colombo, Elisabetta, Paola Frediani, and Giuseppe Pareschi. "Hyperplane sections of abelian surfaces." Journal of Algebraic Geometry 21, no. 1 (January 1, 2012): 183–200. http://dx.doi.org/10.1090/s1056-3911-2011-00556-0.

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15

Michael, A. A. George. "Finite Abelian actions on surfaces." Topology and its Applications 153, no. 14 (August 2006): 2591–612. http://dx.doi.org/10.1016/j.topol.2005.05.010.

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16

Shafarevich, I. R. "Some families of Abelian surfaces." Izvestiya: Mathematics 60, no. 5 (October 31, 1996): 1083–93. http://dx.doi.org/10.1070/im1996v060n05abeh000092.

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17

Sankaran, G. K. "Moduli of Polarised Abelian Surfaces." Mathematische Nachrichten 188, no. 1 (1997): 321–40. http://dx.doi.org/10.1002/mana.19971880117.

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18

Laface, Roberto. "Decompositions of singular abelian surfaces." Asian Journal of Mathematics 23, no. 1 (2019): 157–72. http://dx.doi.org/10.4310/ajm.2019.v23.n1.a8.

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19

Beauville, Arnaud. "Ulrich bundles on abelian surfaces." Proceedings of the American Mathematical Society 144, no. 11 (April 20, 2016): 4609–11. http://dx.doi.org/10.1090/proc/13091.

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20

Yanagida, Shintarou, and Kōta Yoshioka. "Bridgeland’s stabilities on abelian surfaces." Mathematische Zeitschrift 276, no. 1-2 (September 28, 2013): 571–610. http://dx.doi.org/10.1007/s00209-013-1214-1.

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21

Sawin, William F. "Ordinary primes for Abelian surfaces." Comptes Rendus Mathematique 354, no. 6 (June 2016): 566–68. http://dx.doi.org/10.1016/j.crma.2016.01.025.

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22

Kani, Ernst. "Elliptic curves on abelian surfaces." Manuscripta Mathematica 84, no. 1 (December 1994): 199–223. http://dx.doi.org/10.1007/bf02567454.

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23

Lange, H. "Abelian surfaces in ?1�?3." Archiv der Mathematik 63, no. 1 (July 1994): 80–84. http://dx.doi.org/10.1007/bf01196302.

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24

Rasmussen, Christopher, and Akio Tamagawa. "Abelian surfaces good away from 2." International Journal of Number Theory 13, no. 04 (March 24, 2017): 991–1001. http://dx.doi.org/10.1142/s179304211750052x.

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Fix a number field [Formula: see text] and a rational prime [Formula: see text]. We consider abelian varieties whose [Formula: see text]-power torsion generates a pro-[Formula: see text] extension of [Formula: see text] which is unramified away from [Formula: see text]. It is a necessary, but not generally sufficient, condition that such varieties have good reduction away from [Formula: see text]. In the special case of [Formula: see text], we demonstrate that for abelian surfaces [Formula: see text], good reduction away from [Formula: see text] does suffice. The result is extended to elliptic curves and abelian surfaces over certain number fields unramified away from [Formula: see text]. An explicit example is constructed to demonstrate that good reduction away from [Formula: see text] is not sufficient, at [Formula: see text], for abelian varieties of sufficiently high dimension.
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25

Marini, Alfio. "On a family of (1,7)-polarised abelian surfaces." MATHEMATICA SCANDINAVICA 95, no. 2 (December 1, 2004): 181. http://dx.doi.org/10.7146/math.scand.a-14456.

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We study the geometry of the moduli space of $(1,7)$-polarised abelian surfaces with canonical level structure in detail. In particular we describe the locus where the syzygies of the embedded Heisenberg-invariant abelian surface degenerate, and relate this to the other known descriptions of the moduli space in question.
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26

Melliez, F., and K. Ranestad. "Degenerations of $(1,7)$-polarized abelian surfaces." MATHEMATICA SCANDINAVICA 97, no. 2 (December 1, 2005): 161. http://dx.doi.org/10.7146/math.scand.a-14970.

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The moduli space of $(1,7)$-polarized abelian surfaces with a level structure was shown by Manolache and Schreyer to be rational with compactification the variety of powersum presentations of the Klein quartic curve. In this paper the possible degenerations of the abelian surfaces corresponding to degenerations of powersum presentations are classified.
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27

Hulek, K., I. Nieto, and G. K. Sankaran. "Heisenberg-invariant kummer surfaces." Proceedings of the Edinburgh Mathematical Society 43, no. 2 (June 2000): 425–39. http://dx.doi.org/10.1017/s0013091500021015.

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AbstractWe study, from the point of view of abelian and Kummer surfaces and their moduli, the special quintic threefold known as Nieto's quintic. It is, in some ways, analogous to the Segre cubic and the Burkhardt quartic and can be interpreted as a moduli space of certain Kummer surfaces. It contains 30 planes and has 10 singular points: we describe how some of these arise from bielliptic and product abelian surfaces and their Kummer surfaces.
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28

IBUKIYAMA, Tomoyoshi. "Principal polarizations of supersingular abelian surfaces." Journal of the Mathematical Society of Japan 72, no. 4 (October 2020): 1161–80. http://dx.doi.org/10.2969/jmsj/82528252.

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29

Calegari, Frank, Shiva Chidambaram, and David P. Roberts. "Abelian surfaces with fixed 3-torsion." Open Book Series 4, no. 1 (December 29, 2020): 91–108. http://dx.doi.org/10.2140/obs.2020.4.91.

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30

Faye, Ibrahima. "SEMI-ABELIAN SURFACES AND INTEGRABLE SYSTEMS." Proceedings of the Edinburgh Mathematical Society 44, no. 2 (June 2001): 249–65. http://dx.doi.org/10.1017/s0013091599000565.

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AbstractWe study some weight-homogeneous systems which are not algebraically completely integrable (ACI) in the sense of Adler and van Moerebeke, but whose invariant level surface completes into a semi-abelian variety by adding a set of points (thus ACI in the sense of Mumford).AMS 2000 Mathematics subject classification: Primary 37J35. Secondary 14H70; 37N05; 70E40
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31

Yu, Chia-Fu. "Endomorphism algebras of QM abelian surfaces." Journal of Pure and Applied Algebra 217, no. 5 (May 2013): 907–14. http://dx.doi.org/10.1016/j.jpaa.2012.09.022.

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32

Enge, Andreas, and Emmanuel Thomé. "Computing Class Polynomials for Abelian Surfaces." Experimental Mathematics 23, no. 2 (April 3, 2014): 129–45. http://dx.doi.org/10.1080/10586458.2013.878675.

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33

Taylor, Noah. "Sato-Tate distributions on Abelian surfaces." Transactions of the American Mathematical Society 373, no. 5 (February 20, 2020): 3541–59. http://dx.doi.org/10.1090/tran/8025.

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34

Bruin, Nils. "Visualising Sha[2] in Abelian surfaces." Mathematics of Computation 73, no. 247 (January 8, 2004): 1459–77. http://dx.doi.org/10.1090/s0025-5718-04-01633-3.

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35

Jakob, Bernd. "Poncelet 5-gons and abelian surfaces." Manuscripta Mathematica 83, no. 1 (December 1994): 183–98. http://dx.doi.org/10.1007/bf02567608.

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36

Liedtke, Christian. "Singular abelian covers of algebraic surfaces." manuscripta mathematica 112, no. 3 (November 1, 2003): 375–90. http://dx.doi.org/10.1007/s00229-003-0408-y.

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37

Yu, Chia-Fu, and Jeng-Daw Yu. "Mass formula for supersingular abelian surfaces." Journal of Algebra 322, no. 10 (November 2009): 3733–43. http://dx.doi.org/10.1016/j.jalgebra.2009.08.008.

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38

Yoshioka, Kōta. "Fourier–Mukai transform on abelian surfaces." Mathematische Annalen 345, no. 3 (March 27, 2009): 493–524. http://dx.doi.org/10.1007/s00208-009-0356-2.

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39

Sankaran, G. K. "Abelian surfaces in toric 4-folds." Mathematische Annalen 313, no. 3 (March 1, 1999): 409–27. http://dx.doi.org/10.1007/s002080050267.

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40

Tokunaga, H., and H. Yoshihara. "Degree of Irrationality of Abelian Surfaces." Journal of Algebra 174, no. 3 (June 1995): 1111–21. http://dx.doi.org/10.1006/jabr.1995.1170.

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41

Yang, Tonghai. "The Chowla–Selberg Formula and The Colmez Conjecture." Canadian Journal of Mathematics 62, no. 2 (April 1, 2010): 456–72. http://dx.doi.org/10.4153/cjm-2010-028-x.

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AbstractIn this paper, we reinterpret the Colmez conjecture on the Faltings height of CM abelian varieties in terms of Hilbert (and Siegel) modular forms. We construct an elliptic modular form involving the Faltings height of a CM abelian surface and arithmetic intersection numbers, and prove that the Colmez conjecture for CM abelian surfaces is equivalent to the cuspidality of this modular form.
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42

Mehran, Afsaneh. "Kummer surfaces associated to (1, 2)-polarized abelian surfaces." Nagoya Mathematical Journal 202 (June 2011): 127–43. http://dx.doi.org/10.1017/s002776300001028x.

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AbstractThe aim of this paper is to describe the geometry of the generic Kummer surface associated to a (1, 2)-polarized abelian surface. We show that it is the double cover of a weak del Pezzo surface and that it inherits from the del Pezzo surface an interesting elliptic fibration with twelve singular fibers of typeI2.
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43

Mehran, Afsaneh. "Kummer surfaces associated to (1, 2)-polarized abelian surfaces." Nagoya Mathematical Journal 202 (June 2011): 127–43. http://dx.doi.org/10.1215/00277630-1260477.

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AbstractThe aim of this paper is to describe the geometry of the generic Kummer surface associated to a (1, 2)-polarized abelian surface. We show that it is the double cover of a weak del Pezzo surface and that it inherits from the del Pezzo surface an interesting elliptic fibration with twelve singular fibers of type I2.
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44

Alexeev, Valery, and Rita Pardini. "Non-normal abelian covers." Compositio Mathematica 148, no. 4 (March 20, 2012): 1051–84. http://dx.doi.org/10.1112/s0010437x11007482.

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AbstractAn abelian cover is a finite morphism X→Y of varieties which is the quotient map for a generically faithful action of a finite abelian group G. Abelian covers with Y smooth and X normal were studied in [R. Pardini, Abelian covers of algebraic varieties, J. Reine Angew. Math. 417 (1991), 191–213; MR 1103912(92g:14012)]. Here we study the non-normal case, assuming that X and Y are S2 varieties that have at worst normal crossings outside a subset of codimension greater than or equal to two. Special attention is paid to the case of ℤr2-covers of surfaces, which is used in [V. Alexeev and R. Pardini, Explicit compactifications of moduli spaces of Campedelli and Burniat surfaces, Preprint (2009), math.AG/arXiv:0901.4431] to construct explicitly compactifications of some components of the moduli space of surfaces of general type.
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45

Katsura, Toshiyuki, and Katsuyuki Takashima. "Counting Richelot isogenies between superspecial abelian surfaces." Open Book Series 4, no. 1 (December 29, 2020): 283–300. http://dx.doi.org/10.2140/obs.2020.4.283.

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46

Brumer, Armand, Ariel Pacetti, Cris Poor, Gonzalo Tornaría, John Voight, and David Yuen. "On the paramodularity of typical abelian surfaces." Algebra & Number Theory 13, no. 5 (July 12, 2019): 1145–95. http://dx.doi.org/10.2140/ant.2019.13.1145.

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47

Dieulefait, Luis V., and Victor Rotger. "On abelian surfaces with potential quaternionic multiplication." Bulletin of the Belgian Mathematical Society - Simon Stevin 12, no. 4 (December 2005): 617–24. http://dx.doi.org/10.36045/bbms/1133793348.

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48

Kajiwara, Takeshi. "Abelian surfaces in projective toric 4-folds." Archiv der Mathematik 86, no. 1 (January 2006): 43–49. http://dx.doi.org/10.1007/s00013-005-1453-4.

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49

Bertrand, D., D. Masser, A. Pillay, and U. Zannier. "Relative Manin–Mumford for Semi-Abelian Surfaces." Proceedings of the Edinburgh Mathematical Society 59, no. 4 (January 18, 2016): 837–75. http://dx.doi.org/10.1017/s0013091515000486.

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AbstractWe show that Ribet sections are the only obstruction to the validity of the relative Manin–Mumford conjecture for one-dimensional families of semi-abelian surfaces. Applications include special cases of the Zilber–Pink conjecture for curves in a mixed Shimura variety of dimension 4, as well as the study of polynomial Pell equations with non-separable discriminants.
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50

Talu, Y. "Abelian $p$-Groups of Symmetries of Surfaces." Taiwanese Journal of Mathematics 15, no. 3 (June 2011): 1129–40. http://dx.doi.org/10.11650/twjm/1500406290.

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