Academic literature on the topic 'Riemann-Roch theorem'
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Journal articles on the topic "Riemann-Roch theorem"
Das, Mrinal Kanti, and Satya Mandal. "A Riemann–Roch theorem." Journal of Algebra 301, no. 1 (July 2006): 148–64. http://dx.doi.org/10.1016/j.jalgebra.2005.10.007.
Full textHoyois, Marc, Pavel Safronov, Sarah Scherotzke, and Nicolò Sibilla. "The categorified Grothendieck–Riemann–Roch theorem." Compositio Mathematica 157, no. 1 (January 2021): 154–214. http://dx.doi.org/10.1112/s0010437x20007642.
Full textNori, Madhav V. "The Hirzebruch-Riemann-Roch theorem." Michigan Mathematical Journal 48, no. 1 (2000): 473–82. http://dx.doi.org/10.1307/mmj/1030132729.
Full textGillet, Henri, and Christophe Soul�. "An arithmetic Riemann-Roch theorem." Inventiones Mathematicae 110, no. 1 (December 1992): 473–543. http://dx.doi.org/10.1007/bf01231343.
Full textPappas, Georgios. "Integral Grothendieck–Riemann–Roch theorem." Inventiones mathematicae 170, no. 3 (July 18, 2007): 455–81. http://dx.doi.org/10.1007/s00222-007-0067-9.
Full textNavarro, Alberto. "On Grothendieck’s Riemann–Roch theorem." Expositiones Mathematicae 35, no. 3 (September 2017): 326–42. http://dx.doi.org/10.1016/j.exmath.2016.09.005.
Full textPaule, Peter, and Cristian-Silviu Radu. "A Proof of the Weierstraß Gap Theorem not Using the Riemann–Roch Formula." Annals of Combinatorics 23, no. 3-4 (November 2019): 963–1007. http://dx.doi.org/10.1007/s00026-019-00459-2.
Full textJØRGENSEN, PETER. "NON-COMMUTATIVE CURVES AND THEIR ZETA FUNCTIONS." Journal of Algebra and Its Applications 01, no. 02 (June 2002): 175–99. http://dx.doi.org/10.1142/s0219498802000094.
Full textDouglas, Ronald G., Xiang Tang, and Guoliang Yu. "An analytic Grothendieck Riemann Roch theorem." Advances in Mathematics 294 (May 2016): 307–31. http://dx.doi.org/10.1016/j.aim.2016.02.031.
Full textRamadoss, Ajay C. "A generalized Hirzebruch Riemann–Roch theorem." Comptes Rendus Mathematique 347, no. 5-6 (March 2009): 289–92. http://dx.doi.org/10.1016/j.crma.2009.01.015.
Full textDissertations / Theses on the topic "Riemann-Roch theorem"
Shklyarov, Dmytro. "Hirzebruch-Riemann-Roch theorem for differential graded algebras." Diss., Manhattan, Kan. : Kansas State University, 2009. http://hdl.handle.net/2097/1381.
Full textSchulze, Bert-Wolfgang, and Nikolai Tarkhanov. "The Riemann-Roch theorem for manifolds with conical singularities." Universität Potsdam, 1997. http://opus.kobv.de/ubp/volltexte/2008/2505/.
Full textXu, Quan. "On Deligne's functorial Riemann-Roch theorem in positive characteristic." Toulouse 3, 2014. http://thesesups.ups-tlse.fr/2365/.
Full textIn this note, we give a proof for a variant of the functorial Deligne-Riemann-Roch theorem in positive characteristic based on ideas appearing in Pink and Rössler's proof of the Adams-Riemann-Roch theorem in positive characteristic (see [14]). The method of their proof appearing in [14], which is valid for any positive characteristic and which is completely different from the classical proof, will allow us to prove the functorial Deligne-Riemann-Roch theorem in a much easier and more direct way. Our proof is also partially compatible with Mumford's isomorphism
Hahn, Tobias. "An arithmetic Riemann-Roch theorem for metrics with cusps." Aachen Shaker, 2009. http://d-nb.info/997223146/04.
Full textDe, Gaetano Giovanni. "A regularized arithmetic Riemann-Roch theorem via metric degeneration." Doctoral thesis, Humboldt-Universität zu Berlin, 2018. http://dx.doi.org/10.18452/19227.
Full textThe main result of the dissertation is an arithmetic Riemann-Roch theorem for the hermitian line bundle of cusp form of given even integer weights on an arithmetic surface whose complex fiber is isometric to an hyperbolic Riemann surface without elliptic points. The proof proceeds by metric degeneration: We regularize the metric under consideration in a neighborhood of the singularities, then we apply the arithmetic Riemann-Roch theorem of Gillet and Soulé, and finally we let the parameter go to zero. Both sides of the formula blow up through metric degeneration. On one side the exact asymptotic expansion is computed from the definition of the smooth arithmetic intersection numbers. The divergent term on the other side is the zeta-regularized determinant of the Laplacian acting on 1-forms with values in the chosen hermitian line bundle associated to the regularized metrics. We first define and compute a regularization of the determinant of the corresponding Laplacian associated to the singular metrics, which will later occur int he regularized arithmetic Riemann-Roch theorem. To do so we adapt and generalize ideas od Jorgenson-Lundelius, D'Hoker-Phong, and Sarnak. Then, we prove a formula for the on-diagonal heat kernel associated to the chosen hermitian line bundle on a model cusp, from which its behavior close to a cusp is transparent. This expression is related to an expansion in terms of eigenfunctions associated to the Whittaker equation, which we prove in an appendix. Further estimates on the heat kernel associated to the chosen hermitian line bundle on the complex fiber of the arithmetic surface prove the main theorem.
Arruda, Rafael Lucas de [UNESP]. "Teorema de Riemann-Roch e aplicações." Universidade Estadual Paulista (UNESP), 2011. http://hdl.handle.net/11449/86493.
Full textFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
O objetivo principal deste trabalho é estudar o Teorema de Riemann-Roch, um dos resultados fundamentais na teoria de curvas algébricas, e apresentar algumas de suas aplicações. Este teorema é uma importante ferramenta para a classificação das curvas algébricas, pois relaciona propriedades algébricas e topológicas. Daremos uma descrição das curvas algébricas de gênero g, 1≤ g ≤ 5, e faremos um breve estudo dos pontos de inflexão de um sistema linear sobre uma curva algébrica
The main purpose of this work is to discuss The Riemann-Roch Theorem, wich is one of the most important results of the theory algebraic curves, and to present some applications. This theorem is an important tool of the classification of algebraic curves, sinces relates algebraic and topological properties. We will describle the algebraic curves of genus g, 1≤ g ≤ 5, and also study inflection points of a linear system on an algebraic curve
Hahn, Tobias [Verfasser]. "An arithmetic Riemann-Roch theorem for metrics with cusps / Tobias Hahn." Aachen : Shaker, 2009. http://d-nb.info/1156518318/34.
Full textArruda, Rafael Lucas de. "Teorema de Riemann-Roch e aplicações /." São José do Rio Preto : [s.n.], 2011. http://hdl.handle.net/11449/86493.
Full textBanca: Eduardo de Sequeira Esteves
Banca: Jéfferson Luiz Rocha Bastos
Resumo: O objetivo principal deste trabalho é estudar o Teorema de Riemann-Roch, um dos resultados fundamentais na teoria de curvas algébricas, e apresentar algumas de suas aplicações. Este teorema é uma importante ferramenta para a classificação das curvas algébricas, pois relaciona propriedades algébricas e topológicas. Daremos uma descrição das curvas algébricas de gênero g, 1≤ g ≤ 5, e faremos um breve estudo dos pontos de inflexão de um sistema linear sobre uma curva algébrica
Abstract: The main purpose of this work is to discuss The Riemann-Roch Theorem, wich is one of the most important results of the theory algebraic curves, and to present some applications. This theorem is an important tool of the classification of algebraic curves, sinces relates algebraic and topological properties. We will describle the algebraic curves of genus g, 1≤ g ≤ 5, and also study inflection points of a linear system on an algebraic curve
Mestre
Porto, Anderson Corrêa. "Divisores sobre curvas e o Teorema de Riemann-Roch." Universidade Federal de Juiz de Fora (UFJF), 2018. https://repositorio.ufjf.br/jspui/handle/ufjf/6612.
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O objetivo desse trabalho é o estudo de conceitos básicos da Geometria Algébrica sob o ponto de vista clássico. O foco central do trabalho é o estudo do Teorema de Riemann- Roch e algumas de suas aplicações. Esse teorema constitui uma importante ferramenta no estudo da Geometria Algébrica clássica uma vez que possibilita, por exemplo, o cáculo do gênero de uma curva projetiva não singular no espaço projetivo de dimensão dois. Para o desenvolvimento do estudo do Teorema de Riemann-Roch e suas aplicações serão estudados conceitos tais como: variedades, dimensão, diferenciais de Weil, divisores, divisores sobre curvas e o anel topológico Adèle.
The goal of this work is the study of basic concepts of Algebraic Geometry from the classical point of view. The central focus of the paper is the study of Riemann-Roch Theorem and some of its applications. This theorem constitutes an important tool in the study of classical Algebraic Geometry since it allows, for example, the calculation of the genus of a non-singular projective curve in the projective space of dimension two. For the development of the study of the Riemann-Roch Theorem and its applications we will study concepts such as: varieties, dimension, Weil differentials, divisors, divisors on curves and the Adèle topological ring.
Kramer, Jürg [Gutachter], and Gerard [Gutachter] Freixas. "A regularized arithmetic Riemann-Roch theorem via metric degeneration / Gutachter: Jürg Kramer, Gerard Freixas." Berlin : Humboldt-Universität zu Berlin, 2018. http://d-nb.info/1182540503/34.
Full textBooks on the topic "Riemann-Roch theorem"
Faltings, Gerd. Lectures on the arithmetic Riemann-Roch theorem. Princeton, N.J: Princeton University Press, 1992.
Find full textAitken, Wayne. An arithmetic Riemann-Roch theorem for singular arithmetic surfaces. Providence, R.I: American Mathematical Society, 1996.
Find full textKha, Minh, and Peter Kuchment. Liouville-Riemann-Roch Theorems on Abelian Coverings. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-67428-1.
Full textBárcenas, Noé, and Monica Moreno Rocha. Mexican mathematicians abroad: Recent contributions : first workshop, Matematicos Mexicanos Jovenes en el Mundo, August 22-24, 2012, Centro de Investigacion en Matematicas, A.C., Guanajuato, Mexico. Edited by Galaz-García Fernando editor. Providence, Rhode Island: American Mathematical Society, 2016.
Find full textJeremy, Gray. The Riemann-Roch Theorem: 100 Years of Algebra and Geometry. World Scientific Pub Co Inc, 2001.
Find full textFaltings, Gerd. Lectures on the Arithmetic Riemann-Roch Theorem. (AM-127), Volume 127. Princeton University Press, 2016.
Find full textBismut, Jean-Michel. Hypoelliptic Laplacian and Bott-Chern Cohomology: A Theorem of Riemann-Roch-Grothendieck in Complex Geometry. Springer International Publishing AG, 2015.
Find full textBismut, Jean-Michel. Hypoelliptic Laplacian and Bott–Chern Cohomology: A Theorem of Riemann–Roch–Grothendieck in Complex Geometry. Birkhäuser, 2013.
Find full textBook chapters on the topic "Riemann-Roch theorem"
Tsfasman, M. A., and S. G. Vlăduţ. "Riemann-Roch Theorem." In Algebraic-Geometric Codes, 141–67. Dordrecht: Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-011-3810-9_5.
Full textFulton, William. "The Riemann—Roch Theorem." In Graduate Texts in Mathematics, 295–311. New York, NY: Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4612-4180-5_21.
Full textA’Campo, Norbert, Vincent Alberge, and Elena Frenkel. "The Riemann–Roch Theorem." In From Riemann to Differential Geometry and Relativity, 389–411. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-60039-0_13.
Full textLorenzini, Dino. "The Riemann-Roch Theorem." In Graduate Studies in Mathematics, 305–38. Providence, Rhode Island: American Mathematical Society, 1996. http://dx.doi.org/10.1090/gsm/009/10.
Full textVarolin, Dror. "The Riemann-Roch Theorem." In Graduate Studies in Mathematics, 211–21. Providence, Rhode Island: American Mathematical Society, 2011. http://dx.doi.org/10.1090/gsm/125/13.
Full textPopescu-Pampu, Patrick. "The Riemann–Roch Theorem." In What is the Genus?, 43–44. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-42312-8_16.
Full textCiliberto, Ciro. "The Riemann–Roch Theorem." In UNITEXT, 301–19. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-71021-7_20.
Full textHolme, Audun. "The Riemann-Roch Theorem." In A Royal Road to Algebraic Geometry, 329–34. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-19225-8_20.
Full textWeil, André. "The theorem of Riemann-Roch." In Basic Number Theory, 96–101. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-61945-8_6.
Full textLang, Serge. "The Faltings Riemann-Roch Theorem." In Introduction to Arakelov Theory, 102–30. New York, NY: Springer New York, 1988. http://dx.doi.org/10.1007/978-1-4612-1031-3_5.
Full textConference papers on the topic "Riemann-Roch theorem"
DIEP, DO NGOC. "RIEMANN-ROCH THEOREM AND INDEX THEOREM IN NON-COMMUTATIVE GEOMETRY." In Proceedings of the International Conference. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702548_0003.
Full textKasparian, Azniv. "Riemann-Roch Theorem and Mac Williams identities for an additive code with respect to a saturated lattice." In 2020 Algebraic and Combinatorial Coding Theory (ACCT). IEEE, 2020. http://dx.doi.org/10.1109/acct51235.2020.9383243.
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