@article{ASENS_1981_4_14_2_157_0, author = {Gross, Benedict H. and Harris, Joe}, title = {Real algebraic curves}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, pages = {157--182}, publisher = {Elsevier}, volume = {Ser. 4, 14}, number = {2}, year = {1981}, doi = {10.24033/asens.1401}, mrnumber = {83a:14028}, zbl = {0533.14011}, language = {en}, url = {https://www.numdam.org/articles/10.24033/asens.1401/} }
TY - JOUR AU - Gross, Benedict H. AU - Harris, Joe TI - Real algebraic curves JO - Annales scientifiques de l'École Normale Supérieure PY - 1981 SP - 157 EP - 182 VL - 14 IS - 2 PB - Elsevier UR - https://www.numdam.org/articles/10.24033/asens.1401/ DO - 10.24033/asens.1401 LA - en ID - ASENS_1981_4_14_2_157_0 ER -
Gross, Benedict H.; Harris, Joe. Real algebraic curves. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 14 (1981) no. 2, pp. 157-182. doi : 10.24033/asens.1401. https://www.numdam.org/articles/10.24033/asens.1401/
[1] Sur la première partie du seizième problème de Hilbert (Sém. Bourbaki, exposé 537, 1979). | Numdam | Zbl
,[2] Riemann Surfaces and Spin Structures (Ann. Éc. Norm. Sup., T. 4, 4e serie, 1971, pp. 47-62). | Numdam | MR | Zbl
,[3] Principles of Algebraic Geometry, New York, Wiley, 1978. | MR | Zbl
and ,[4] Arithmetic on Elliptic Curves with Complex Multiplication (Lecture Notes, No. 776, Springer, 1980). | MR | Zbl
,[5] Über eindeutige 2n-fach periodische Funktionen (Math. Werke I., 1932, pp. 99-116).
,[6] Symmetric Bilinear Forms, New York, Springer, 1973. | MR | Zbl
and ,[7] On Riemann's Theory of Algebraic Functions and Their Integrals, Cambridge, Macmillan and Bowes, 1893.
,[8] Ueber Realitätsverhältnisse bei der einem beliebigen Geschlechte zugehoren Normalcurve der ϕ (Math. Ann., Vol. 42, 1893, pp. 1-29). | JFM
,[9] Principal Homogeneous Spaces Over Abelian Varieties (Amer. J. Math., Vol. 80, pp. 659-684). | MR | Zbl
and ,[10] A New Proof of Torelli's Theorem (Annals of Math., Vol. 78 1963, pp. 107-111). | MR | Zbl
,[11] Theta Characteristics of An Algebraic Curve (Ann. Éc. Norm. Sup., T. 4, 4e série, 1971, pp. 181-192). | EuDML | Numdam | MR | Zbl
,[12] Quotients of Complex Manifolds and Moduli Spaces of Klein Surfaces (Preprint). | Zbl
,[13] Groupes algébriques et corps de classes, Hermann, Paris, 1959. | MR | Zbl
,[14] On the Real Points of an Arithmetic quotient of a Bounded Symmetric Domain (Math. Ann., Vol. 215, 1975, pp. 135-164). | EuDML | MR | Zbl
,[15] W.C. Groups Over p-Adic Fields (Sém. Bourbaki, exposé 156, 1957). | EuDML | Numdam | MR | Zbl
,[16] Uber symmetrische Riemannsche Flachen (Zeit f. Math. u. Phys., Vol. 28, 1883, pp. 321-351). | JFM
,[17] The Field of Definition of a Variety (Amer. J. Math., Vol. 78, 1956, pp. 509-524). | MR | Zbl
,[18] Hilbert's Sixteenth Problem (Topology, Vol. 17, 1978, pp. 53-73). | MR | Zbl
,[19] Zerlegung reeller algebraischer Funktionen in Quadrate (J. Crelle., Vol. 171, 1934, pp. 4-11). | EuDML | JFM | Zbl
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- Real structures on primary Hopf surfaces, Complex Manifolds, Volume 11 (2024) no. 1 | DOI:10.1515/coma-2024-0007
- On the Algebraic Geometry of Multiview, Foundations, Volume 4 (2024) no. 3, p. 306 | DOI:10.3390/foundations4030020
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- Avoidance loci and tropicalizations of real bitangents to plane quartics, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 154 (2024) no. 4, p. 1308 | DOI:10.1017/prm.2023.67
- Bounding the signed count of real bitangents to plane quartics, manuscripta mathematica, Volume 173 (2024) no. 3-4, p. 1003 | DOI:10.1007/s00229-023-01493-4
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- Combinatorics and Real Lifts of Bitangents to Tropical Quartic Curves, Discrete Computational Geometry, Volume 69 (2023) no. 3, p. 597 | DOI:10.1007/s00454-022-00445-1
- Quadrature for quadrics, European Journal of Mathematics, Volume 9 (2023) no. 4 | DOI:10.1007/s40879-023-00707-z
- On the parity conjecture for abelian surfaces, Proceedings of the London Mathematical Society, Volume 127 (2023) no. 2, p. 295 | DOI:10.1112/plms.12545
- Principal Higgs Bundles and Schottky Representations, Current Trends in Analysis, its Applications and Computation (2022), p. 89 | DOI:10.1007/978-3-030-87502-2_10
- The real Plücker-Klein map, Izvestiya: Mathematics, Volume 86 (2022) no. 3, p. 456 | DOI:10.1070/im9270
- Hyperbolic secant varieties of M-curves, Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2022 (2022) no. 787, p. 125 | DOI:10.1515/crelle-2022-0012
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- Surfaces in the Flag Threefold Containing Smooth Conics and Twistor Fibers, Mediterranean Journal of Mathematics, Volume 19 (2022) no. 6 | DOI:10.1007/s00009-022-02202-3
- The 2-parity conjecture for elliptic curves with isomorphic 2-torsion, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Volume 478 (2022) no. 2265 | DOI:10.1098/rspa.2022.0112
- Real Moduli Spaces And Density Of Non-simple Real Abelian Varieties, The Quarterly Journal of Mathematics, Volume 73 (2022) no. 3, p. 969 | DOI:10.1093/qmath/haab060
- Вещественное отображение Плюккера-Клейна, Известия Российской академии наук. Серия математическая, Volume 86 (2022) no. 3, p. 47 | DOI:10.4213/im9119
- On Huisman’s conjectures about unramified real curves, Advances in Geometry, Volume 21 (2021) no. 4, p. 545 | DOI:10.1515/advgeom-2021-0032
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- On the integral Hodge conjecture for real varieties, I, Inventiones mathematicae, Volume 222 (2020) no. 1, p. 1 | DOI:10.1007/s00222-020-00965-8
- Totally real theta characteristics, Annali di Matematica Pura ed Applicata (1923 -), Volume 198 (2019) no. 6, p. 2141 | DOI:10.1007/s10231-019-00858-5
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- Maximally writhed real algebraic links, Inventiones mathematicae, Volume 216 (2019) no. 1, p. 125 | DOI:10.1007/s00222-018-0844-7
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- Branes through finite group actions, Journal of Geometry and Physics, Volume 129 (2018), p. 279 | DOI:10.1016/j.geomphys.2018.03.014
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- Certifying Reality of Projections, Mathematical Software – ICMS 2018, Volume 10931 (2018), p. 200 | DOI:10.1007/978-3-319-96418-8_24
- О классическом соответствии вещественных К3-поверхностей, Известия Российской академии наук. Серия математическая, Volume 82 (2018) no. 4, p. 18 | DOI:10.4213/im8627
- One-dimensional Schubert Problems with Respect to Osculating Flags, Canadian Journal of Mathematics, Volume 69 (2017) no. 1, p. 143 | DOI:10.4153/cjm-2015-061-1
- A Torelli theorem for moduli spaces of principal bundles on curves defined over ℝ, International Journal of Mathematics, Volume 28 (2017) no. 06, p. 1750049 | DOI:10.1142/s0129167x17500495
- Monodromy and K-theory of Schubert curves via generalized jeu de taquin, Journal of Algebraic Combinatorics, Volume 45 (2017) no. 1, p. 191 | DOI:10.1007/s10801-016-0705-7
- Algebraic K-theory and derived equivalences suggested by T-duality for torus orientifolds, Journal of Pure and Applied Algebra, Volume 221 (2017) no. 7, p. 1717 | DOI:10.1016/j.jpaa.2016.12.025
- Arithmetic invariant theory and 2-descent for plane quartic curves, Algebra Number Theory, Volume 10 (2016) no. 7, p. 1373 | DOI:10.2140/ant.2016.10.1373
- Pencils of quadrics and Gromov–Witten–Welschinger invariants of
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- Selmer groups and class groups, Compositio Mathematica, Volume 151 (2015) no. 3, p. 416 | DOI:10.1112/s0010437x14007441
- Counting Real Rational Curves onK3 Surfaces, International Mathematics Research Notices, Volume 2015 (2015) no. 14, p. 5436 | DOI:10.1093/imrn/rnu091
- Bigraded invariants for real curves, Algebraic Geometric Topology, Volume 14 (2014) no. 5, p. 2809 | DOI:10.2140/agt.2014.14.2809
- Pencils on separating
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- Shimura Curve Quotients with Odd Jacobians, Journal of Number Theory, Volume 87 (2001) no. 1, p. 96 | DOI:10.1006/jnth.2000.2600
- Complex automorphism groups of real algebraic curves of genus 2, Journal of Pure and Applied Algebra, Volume 157 (2001) no. 2-3, p. 157 | DOI:10.1016/s0022-4049(00)00006-2
- Brauer groups of curves and unramified, central simple algebras over their function fields, Journal of Mathematical Sciences, Volume 102 (2000) no. 3, p. 4071 | DOI:10.1007/bf02673881
- Модули вещественных алгебраических кривых и их супераналоги. Дифференциалы, спиноры и якобианы вещественных кривых, Успехи математических наук, Volume 54 (1999) no. 6, p. 3 | DOI:10.4213/rm229
- Morphisms, line bundles and moduli spaces in real algebraic geometry, Publications mathématiques de l'IHÉS, Volume 86 (1997) no. 1, p. 5 | DOI:10.1007/bf02698900
- Halves of a real Enriques surface, Commentarii Mathematici Helvetici, Volume 71 (1996) no. 1, p. 628 | DOI:10.1007/bf02566440
- Real abelian varieties and real algebraic curves, Lectures in Real Geometry (1996), p. 167 | DOI:10.1515/9783110811117.167
- Algebraic Equivalence and Homology Classes of Real Algebraic Cycles, Mathematische Nachrichten, Volume 180 (1996) no. 1, p. 135 | DOI:10.1002/mana.3211800108
- A characterization of dividing real algebraic curves, Topology, Volume 35 (1996) no. 2, p. 451 | DOI:10.1016/0040-9383(95)00024-0
- Classification of real moduli spaces over genus 2 curves, Geometriae Dedicata, Volume 57 (1995) no. 2, p. 207 | DOI:10.1007/bf01264938
- Computation of period matrices of real algebraic curves, Discrete Computational Geometry, Volume 11 (1994) no. 1, p. 65 | DOI:10.1007/bf02573995
- On the number of connected components of real abelian varieties that admit sufficiently many complex multiplications, Manuscripta Mathematica, Volume 85 (1994) no. 1, p. 165 | DOI:10.1007/bf02568191
- Compactifications of moduli spaces in real algebraic geometry, Inventiones Mathematicae, Volume 107 (1992) no. 1, p. 151 | DOI:10.1007/bf01231886
- Vector bundles on a product of real cubic curves, K-Theory, Volume 6 (1992) no. 6, p. 487 | DOI:10.1007/bf00997378
- Moduli problems in real algebraic geometry, Real Algebraic Geometry, Volume 1524 (1992), p. 110 | DOI:10.1007/bfb0084611
- Deformations of real singularities, Topology, Volume 29 (1990) no. 4, p. 441 | DOI:10.1016/0040-9383(90)90015-c
- Moduli spaces for real algebraic curves and real abelian varieties, Mathematische Zeitschrift, Volume 201 (1989) no. 2, p. 151 | DOI:10.1007/bf01160673
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