Abstract
We find the complete integer solutions of the equation
Funding source: Fundação para a Ciência e a Tecnologia
Award Identifier / Grant number: UIDB/00212/2020
Award Identifier / Grant number: UIDB/04674/2020
Funding source: Ministerio de Economía y Competitividad
Award Identifier / Grant number: MTM2016-78623-P
Funding statement: Sérgio Mendes was partially supported by FCT through CMA-UBI (project UIDB/00212/2020). Rosa M. Miró-Roig was partially supported by MTM2016-78623-P. Helena Soares was partially supported by CIMA – Centro de Investigação em Matemática e Aplicações, Universidade de Évora, project UIDB/04674/2020 (Fundação para a Ciência e Tecnologia), and MTM2016-78623-P.
Communicated by: Jan Bruinier
References
[1] E. Ballico, G. Bolondi, P. Ellia and R. M. Mirò-Roig, Curves of maximum genus in range A and stick-figures, Trans. Amer. Math. Soc. 349 (1997), no. 11, 4589–4608. 10.1090/S0002-9947-97-01917-XSearch in Google Scholar
[2]
G. Bohnhorst and H. Spindler,
The stability of certain vector bundles on
[3] M. C. Brambilla, Cokernel bundles and Fibonacci bundles, Math. Nachr. 281 (2008), no. 4, 499–516. 10.1002/mana.200510620Search in Google Scholar
[4] J. W. S. Cassels, Rational Quadratic Forms, Dover, New York, 1978. Search in Google Scholar
[5]
I. Dolgachev and M. Kapranov,
Arrangements of hyperplanes and vector bundles on
[6] D. Eisenbud and S. Goto, Linear free resolutions and minimal multiplicity, J. Algebra 88 (1984), no. 1, 89–133. 10.1016/0021-8693(84)90092-9Search in Google Scholar
[7]
R. Hartshorne and R. M. Miró-Roig,
On the intersection of ACM curves in
[8] K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory, Springer, New York, 1990. 10.1007/978-1-4757-2103-4Search in Google Scholar
[9] M. Jardim and R. V. Martins, Linear and Steiner bundles on projective varieties, Comm. Algebra 38 (2010), no. 6, 2249–2270. 10.1080/00927871003757584Search in Google Scholar
[10]
S. Marchesi and D. M. Prata,
Simplicity and exceptionality of syzygy bundles over
[11] R. M. Miró-Roig and H. Soares, Exceptional bundles of homological dimension 𝑘, Forum Math. 29 (2017), no. 3, 701–715. 10.1515/forum-2015-0058Search in Google Scholar
[12] J.-P. Serre, Cours d’arithmétique, Coll. SUP Le Math. 2, Presses Universitaires de France, Paris, 1970. Search in Google Scholar
[13] H. Soares, Steiner Vector Bundles on Algebraic Varieties, Ph.D. thesis, University of Barcelona, 2008. Search in Google Scholar
[14] A. Weil, Number Theory: An Approach Through History, Birkhäuser, Boston, 1984. Search in Google Scholar
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