Academic literature on the topic 'Holomorphic symplectic manifolds'

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Journal articles on the topic "Holomorphic symplectic manifolds"

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Zehmisch, Kai. "Holomorphic jets in symplectic manifolds." Journal of Fixed Point Theory and Applications 17, no. 2 (2014): 379–402. http://dx.doi.org/10.1007/s11784-014-0178-z.

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Beauville, Arnaud. "Antisymplectic involutions of holomorphic symplectic manifolds." Journal of Topology 4, no. 2 (2011): 300–304. http://dx.doi.org/10.1112/jtopol/jtr002.

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Camere, Chiara. "Lattice polarized irreducible holomorphic symplectic manifolds." Annales de l’institut Fourier 66, no. 2 (2016): 687–709. http://dx.doi.org/10.5802/aif.3022.

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Gromov, M. "Pseudo holomorphic curves in symplectic manifolds." Inventiones Mathematicae 82, no. 2 (1985): 307–47. http://dx.doi.org/10.1007/bf01388806.

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Ali, Danish, Johann Davidov, and Oleg Mushkarov. "Holomorphic curvatures of twistor spaces." International Journal of Geometric Methods in Modern Physics 11, no. 03 (2014): 1450022. http://dx.doi.org/10.1142/s0219887814500224.

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We study the twistor spaces of oriented Riemannian 4-manifolds as a source of almost Hermitian 6-manifolds of constant or strictly positive holomorphic, Hermitian and orthogonal bisectional curvatures. In particular, we obtain explicit formulas for these curvatures in the case when the base manifold is Einstein and self-dual, and observe that the "squashed" metric on ℂℙ3 is a non-Kähler Hermitian–Einstein metric of positive holomorphic bisectional curvature. This shows that a recent result of Kalafat and Koca [M. Kalafat and C. Koca, Einstein–Hermitian 4-manifolds of positive bisectional curva
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Tardini, Nicoletta, and Adriano Tomassini. "On the cohomology of almost-complex and symplectic manifolds and proper surjective maps." International Journal of Mathematics 27, no. 12 (2016): 1650103. http://dx.doi.org/10.1142/s0129167x16501032.

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Let [Formula: see text] be an almost-complex manifold. In [Comparing tamed and compatible symplectic cones and cohomological properties of almost-complex manifolds, Comm. Anal. Geom. 17 (2009) 651–683], Li and Zhang introduce [Formula: see text] as the cohomology subgroups of the [Formula: see text]th de Rham cohomology group formed by classes represented by real pure-type forms. Given a proper, surjective, pseudo-holomorphic map between two almost-complex manifolds, we study the relationship among such cohomology groups. Similar results are proven in the symplectic setting for the cohomology
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Braverman, Maxim. "Symplectic cutting of Kähler manifolds." Journal für die reine und angewandte Mathematik (Crelles Journal) 1999, no. 508 (1999): 85–98. http://dx.doi.org/10.1515/crll.1999.508.85.

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Abstract We obtain estimates on the character of the cohomology of an S1-equivariant holomorphic vector bundle over a Kähler manifold M in terms of the cohomology of the Lerman symplectic cuts and the symplectic reduction of M. In particular, we prove and extend inequalities conjectured by Wu and Zhang. The proof is based on constructing a flat family of complex spaces Mt (t ∈ ℂ) such that Mt is isomorphic to M for t ≠ 0, while M0 is a singular reducible complex space, whose irreducible components are the Lerman symplectic cuts.
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Boissière, Samuel, Marc Nieper-Wißkirchen, and Alessandra Sarti. "Smith theory and irreducible holomorphic symplectic manifolds." Journal of Topology 6, no. 2 (2013): 361–90. http://dx.doi.org/10.1112/jtopol/jtt002.

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Franco, Emilio, Marcos Jardim, and Grégoire Menet. "Brane involutions on irreducible holomorphic symplectic manifolds." Kyoto Journal of Mathematics 59, no. 1 (2019): 195–235. http://dx.doi.org/10.1215/21562261-2018-0009.

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Ran, Ziv. "Deformations of holomorphic pseudo-symplectic Poisson manifolds." Advances in Mathematics 304 (January 2017): 1156–75. http://dx.doi.org/10.1016/j.aim.2016.09.016.

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Dissertations / Theses on the topic "Holomorphic symplectic manifolds"

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Cattaneo, Alberto. "Non-symplectic automorphisms of irreducible holomorphic symplectic manifolds." Thesis, Poitiers, 2018. http://www.theses.fr/2018POIT2322/document.

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Nous allons étudier les automorphismes des variétés symplectiques holomorphes irréductibles de type K3^[n], c'est-à-dire des variétés équivalentes par déformation au schéma de Hilbert de n points sur une surface K3, pour n > 1.Dans la première partie de la thèse, nous classifions les automorphismes du schéma de Hilbert de n points sur une surface K3 projective générique, dont le réseau de Picard est engendré par un fibré ample. Nous montrons que le groupe des automorphismes est soit trivial soit engendré par une involution non-symplectique et nous déterminons des conditions numériques et gé
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Onorati, Claudio. "Irreducible holomorphic symplectic manifolds and monodromy operators." Thesis, University of Bath, 2018. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.767583.

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One of the most important tools to study the geometry of irreducible holomorphic symplectic manifolds is the monodromy group. The first part of this dissertation concerns the construction and studyof monodromy operators on irreducible holomorphic symplectic manifolds which are deformation equivalent to the 10-dimensional example constructed by O'Grady. The second part uses the knowledge of the monodromy group to compute the number of connected components of moduli spaces of bothmarked and polarised irreducible holomorphic symplectic manifolds which are deformationequivalent to generalised Kumm
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Istrati, Nicolina. "Conformal structures on compact complex manifolds." Thesis, Sorbonne Paris Cité, 2018. http://www.theses.fr/2018USPCC054/document.

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Dans cette thèse on s’intéresse à deux types de structures conformes non-dégénérées sur une variété complexe compacte donnée. La première c’est une forme holomorphe symplectique twistée (THS), i.e. une deux-forme holomorphe non-dégénérée à valeurs dans un fibré en droites. Dans le deuxième contexte, il s’agit des métriques localement conformément kähleriennes (LCK). Dans la première partie, on se place sur un variété de type Kähler. Les formes THS généralisent les formes holomorphes symplectiques, dont l’existence équivaut à ce que la variété admet une structure hyperkählerienne, par un théorè
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Krestiachine, Alexandre. "Donaldson hypersurfaces and Gromov-Witten invariants." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2015. http://dx.doi.org/10.18452/17346.

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Die Frage nach dem Verstäandnis der Topologie symplektischer Mannigfaltigkeiten erhielt immer größere Aufmerksamkeit, insbesondere seit den Arbeiten von A. Weinstein und V. Arnold. Ein bewährtes Mittel ist dabei die Theorie der Gromov-Witten-Invarianten. Eine Gromov-Witten-Invariante zählt Schnitte von rationalen Zyklen mit Modulräumen J-holomorpher Kurven, die eine fixierte Homologieklasse repräsentieren, für eine zahme fast komplexe Struktur. Allerdings ist es im Allgemeinen schwierig, solche Schnittzahlen zu definieren, ohne zusätzliche Annahmen an die symplektische Mannigfaltigkeit zu tref
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Books on the topic "Holomorphic symplectic manifolds"

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McDuff, Dusa. J-holomorphic curves and symplectic topology. American Mathematical Society, 2004.

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(Dietmar), Salamon D., ed. J-holomorphic curves and symplectic topology. 2nd ed. American Mathematical Society, 2012.

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McDuff, Dusa. J-holomorphic curves and quantum cohomology. American Mathematical Society, 1994.

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Ibragimov, Zair. Topics in several complex variables: First USA-Uzbekistan Conference on Analysis and Mathematical Physics, May 20-23, 2014, California State University, Fullerton, California. American Mathematical Society, 2016.

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Michèle, Audin, and Lafontaine, J. 1944 Mar. 10-, eds. Holomorphic curves in symplectic geometry. Birkhäuser, 1994.

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Wendl, Chris. Holomorphic Curves in Low Dimensions: From Symplectic Ruled Surfaces to Planar Contact Manifolds. Springer, 2018.

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McDuff, Dusa, and Dietmar Salamon. Almost complex structures. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198794899.003.0005.

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The chapter begins with a general discussion of almost complex structures on symplectic manifolds and then addresses the problem of integrability. Subsequent sections discuss a variety of examples of Kähler manifolds, in particular those of complex dimension two, and show how to compute the Chern classes and Betti numbers of hypersurfaces in complex projective space. The last section is a brief introduction to the theory of J-holomorphic curves.
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McDuff, Dusa, and Dietmar Salamon. Introduction to Symplectic Topology. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198794899.001.0001.

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Over the past number of years powerful new methods in analysis and topology have led to the development of the modern global theory of symplectic topology, including several striking and important results. The first edition of Introduction to Symplectic Topology was published in 1995. The book was the first comprehensive introduction to the subject and became a key text in the area. In 1998, a significantly revised second edition contained new sections and updates. This third edition includes both further updates and new material on this fast-developing area. All chapters have been revised to
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Holomorphic Morse Inequalities and Bergman Kernels (Progress in Mathematics). Birkhäuser Basel, 2007.

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Book chapters on the topic "Holomorphic symplectic manifolds"

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Audin, Michèle. "Symplectic and almost complex manifolds." In Holomorphic Curves in Symplectic Geometry. Birkhäuser Basel, 1994. http://dx.doi.org/10.1007/978-3-0348-8508-9_3.

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Forstnerič, Franc. "Surjective Holomorphic Maps onto Oka Manifolds." In Complex and Symplectic Geometry. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-62914-8_6.

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Sawon, Justin. "Derived equivalence of holomorphic symplectic manifolds." In CRM Proceedings and Lecture Notes. American Mathematical Society, 2004. http://dx.doi.org/10.1090/crmp/038/09.

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Siebert, Bernd, and Gang Tian. "Lectures on Pseudo-Holomorphic Curves and the Symplectic Isotopy Problem." In Symplectic 4-Manifolds and Algebraic Surfaces. Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-78279-7_5.

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de Bartolomeis, Paolo. "ℤ2 and ℤ-Deformation Theory for Holomorphic and Symplectic Manifolds." In Complex, Contact and Symmetric Manifolds. Birkhäuser Boston, 2005. http://dx.doi.org/10.1007/0-8176-4424-5_6.

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Camere, Chiara. "Moduli Spaces of Cubic Threefolds and of Irreducible Holomorphic Symplectic Manifolds." In Birational Geometry and Moduli Spaces. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-37114-2_2.

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"Compact hyper-Kähler manifolds and holomorphic symplectic manifolds." In Chern Numbers and Rozansky–Witten Invariants of Compact Hyper-Kähler Manifolds. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812562357_0001.

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"Closed Holomorphic Curves in Symplectic 4-Manifolds." In Lectures on Contact 3-Manifolds, Holomorphic Curves and Intersection Theory. Cambridge University Press, 2020. http://dx.doi.org/10.1017/9781108608954.003.

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"Symplectic Fillings of Planar Contact 3-Manifolds." In Lectures on Contact 3-Manifolds, Holomorphic Curves and Intersection Theory. Cambridge University Press, 2020. http://dx.doi.org/10.1017/9781108608954.007.

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GUAN, DANIEL (ZHUANG-DAN). "EXAMPLES OF COMPACT HOLOMORPHIC SYMPLECTIC MANIFOLDS WHICH ADMIT NO KÄHLER STRUCTURE." In Geometry and Analysis on Complex Manifolds. WORLD SCIENTIFIC, 1994. http://dx.doi.org/10.1142/9789814350112_0004.

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