Relevant bibliographies by topics / Irreducible holomorphic symplectic manifolds

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters

Academic literature on the topic 'Irreducible holomorphic symplectic manifolds'

Author: Grafiati
Published: 8 June 2024
Last updated: 31 July 2025

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Journal articles on the topic "Irreducible holomorphic symplectic manifolds"

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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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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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Camere, Chiara. "Some remarks on moduli spaces of lattice polarized holomorphic symplectic manifolds." Communications in Contemporary Mathematics 20, no. 04 (2018): 1750044. http://dx.doi.org/10.1142/s0219199717500444.

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We construct quasi-projective moduli spaces of [Formula: see text]-general lattice polarized irreducible holomorphic symplectic manifolds. Moreover, we study their Baily–Borel compactification and investigate a relation between one-dimensional boundary components and equivalence classes of rational Lagrangian fibrations defined on mirror manifolds.
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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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Amerik, Ekaterina, and Misha Verbitsky. "Construction of automorphisms of hyperkähler manifolds." Compositio Mathematica 153, no. 8 (2017): 1610–21. http://dx.doi.org/10.1112/s0010437x17007138.

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Let $M$ be an irreducible holomorphic symplectic (hyperkähler) manifold. If $b_{2}(M)\geqslant 5$, we construct a deformation $M^{\prime }$ of $M$ which admits a symplectic automorphism of infinite order. This automorphism is hyperbolic, that is, its action on the space of real $(1,1)$-classes is hyperbolic. If $b_{2}(M)\geqslant 14$, similarly, we construct a deformation which admits a parabolic automorphism (and many other automorphisms as well).
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Brecan, Ana-Maria, Tim Kirschner, and Martin Schwald. "Unobstructedness of hyperkähler twistor spaces." Mathematische Zeitschrift 300, no. 3 (2021): 2485–517. http://dx.doi.org/10.1007/s00209-021-02841-4.

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AbstractA family of irreducible holomorphic symplectic (ihs) manifolds over the complex projective line has unobstructed deformations if its period map is an embedding. This applies in particular to twistor spaces of ihs manifolds. Moreover, a family of ihs manifolds over a subspace of the period domain extends to a universal family over an open neighborhood in the period domain.
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Camere, Chiara, Grzegorz Kapustka, Michał Kapustka, and Giovanni Mongardi. "Verra Four-Folds, Twisted Sheaves, and the Last Involution." International Mathematics Research Notices 2019, no. 21 (2018): 6661–710. http://dx.doi.org/10.1093/imrn/rnx327.

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Abstract We study the geometry of some moduli spaces of twisted sheaves on K3 surfaces. In particular we introduce induced automorphisms from a K3 surface on moduli spaces of twisted sheaves on this K3 surface. As an application we prove the unirationality of moduli spaces of irreducible holomorphic symplectic manifolds of K3[2]-type admitting non-symplectic involutions with invariant lattices U(2) ⊕ D4(−1) or U(2) ⊕ E8(−2). This complements the results obtained in [43], [13], and the results from [29] about the geometry of irreducible holomorphic symplectic (IHS) four-folds constructed using
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Golla, Marco, and Laura Starkston. "The symplectic isotopy problem for rational cuspidal curves." Compositio Mathematica 158, no. 7 (2022): 1595–682. http://dx.doi.org/10.1112/s0010437x2200762x.

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We define a suitably tame class of singular symplectic curves in 4-manifolds, namely those whose singularities are modeled on complex curve singularities. We study the corresponding symplectic isotopy problem, with a focus on rational curves with irreducible singularities (rational cuspidal curves) in the complex projective plane. We prove that every such curve is isotopic to a complex curve in degrees up to five, and for curves with one singularity whose link is a torus knot. Classification results of symplectic isotopy classes rely on pseudo-holomorphic curves together with a symplectic vers
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Mongardi, Giovanni, Antonio Rapagnetta, and Giulia Saccà. "The Hodge diamond of O’Grady’s six-dimensional example." Compositio Mathematica 154, no. 5 (2018): 984–1013. http://dx.doi.org/10.1112/s0010437x1700803x.

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We realize O’Grady’s six-dimensional example of an irreducible holomorphic symplectic (IHS) manifold as a quotient of an IHS manifold of$\text{K3}^{[3]}$type by a birational involution, thereby computing its Hodge numbers.
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Dissertations / Theses on the topic "Irreducible 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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CATTANEO, ALBERTO. "NON-SYMPLECTIC AUTOMORPHISMS OF IRREDUCIBLE HOLOMORPHIC SYMPLECTIC MANIFOLDS." Doctoral thesis, Università degli Studi di Milano, 2018. http://hdl.handle.net/2434/606455.

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La tesi si concentra sullo studio degli automorfismi di varietà olomorfe simplettiche irriducibili di tipo K3^[n], ovvero varietà equivalenti per deformazione allo schema di Hilbert di n punti su una superficie K3, per n > 1. Negli ultimi anni, molti teoremi classici riguardanti la classificazione degli automorfismi non-simplettici di superfici K3 sono stati estesi alle varietà di tipo K3^[2]. Siamo quindi interessati a comprendere se tali risultati possono essere ulteriormente generalizzati anche al caso di varietà di tipo K3^[n], per n > 2. Nella prima parte della tesi descriviamo il grup
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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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NOVARIO, SIMONE. "LINEAR SYSTEMS ON IRREDUCIBLE HOLOMORPHIC SYMPLECTIC MANIFOLDS." Doctoral thesis, Università degli Studi di Milano, 2021. http://hdl.handle.net/2434/886303.

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In questa tesi studiamo alcuni sistemi lineari completi associati a divisori di schemi di Hilbert di 2 punti su una superficie K3 proiettiva complessa con gruppo di Picard di rango 1, e le mappe razionali indotte. Queste varietà sono chiamate quadrati di Hilbert su superfici K3 generiche, e sono esempi di varietà irriducibili olomorfe simplettiche (varietà IHS). Nella prima parte della tesi, usando la teoria dei reticoli, gli operatori di Nakajima e il modello di Lehn–Sorger, diamo una base per il sottospazio vettoriale dell’anello di coomologia singolare a coefficienti razionali generato dal
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Denisi, Francesco Antonio. "Positivité sur les variétés irréductibles holomorphes symplectiques." Electronic Thesis or Diss., Université de Lorraine, 2023. http://www.theses.fr/2023LORR0162.

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Dans cette thèse, nous étudions certains aspects de la positivité des diviseurs sur les variétés irréductibles holomorphes symplectiques (IHS). Fixons une variété IHS projective X de dimension complexe 2n. Inspirés par le travail de Bauer, Küronya et Szemberg, nous montrons que le cône big de X a une décomposition localement finie en sous-cônes localement rationnelles polyhédraux, qu'on appelle chambres de Boucksom-Zariski. Ces sous-cônes ont une signification géométrique : sur chacun d'eux, la fonction volume est exprimée par un polynôme homogène de degré 2n. De plus, à l'intérieur de toute c
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Joumaah, Malek [Verfasser]. "Automorphisms of irreducible symplectic manifolds / Malek Joumaah." Hannover : Technische Informationsbibliothek und Universitätsbibliothek Hannover (TIB), 2015. http://d-nb.info/1068920580/34.

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Bertini, Valeria. "Rational curves on irreducible symplectic varieties of OG10 type." Thesis, Strasbourg, 2019. https://publication-theses.unistra.fr/public/theses_doctorat/2019/Bertini_Valeria_2019_ED269.pdf.

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Les variétés holomorphes symplectiques irréductibles (VHSI) sont l'analogue algébrique des variétés Riemannienne hyperkähler. Une VHSI X avec dimension 2 est une surface K3, et dans ce cas, si de plus X est projective, chaque courbe ample sur X est linéairement équivalente à une somme de courbes rationnelles (Bogomolov, Mumford). Charles, Mongardi et Pacienza ont démontré l'existence de diviseurs uniréglés dans (presque) tous les systèmes linéaires amples sur une VHSI qui est déformation d'un schéma de Hilbert sur une surface K3 ou d'une variété de Kummer generalisée. La présence de nombreuses
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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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Torres, Ruiz Rafael. "Geography and Botany of Irreducible Symplectic 4-Manifolds with Abelian Fundamental Group." Thesis, 2010. https://thesis.library.caltech.edu/5941/1/thesis_template.pdf.

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<p>In this thesis the geography and botany of irreducible symplectic 4-manifolds with abelian fundamental group of small rank are studied. It resembles an anthology of the contribution obtained by the author during his infatuation with 4-dimensional topology by studying its recent developments. As such, each chapter is independent from each other and the reader is welcomed to start reading whichever one seems more appealing. We now give an outline for the sake of convenience.</p> <p>The first chapter of the thesis deals with the existence and (lack of) uniqueness of smooth irreducible sympl
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Books on the topic "Irreducible 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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Audin, Michèle, and Jacques Lafontaine. Holomorphic Curves in Symplectic Geometry. Springer Basel AG, 2012.

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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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Ma, Xiaonan, and George Marinescu. Holomorphic Morse Inequalities and Bergman Kernels. Springer London, Limited, 2007.

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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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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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Modern Geometry: A Celebration of the Work of Simon Donaldson. American Mathematical Society, 2018.

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Book chapters on the topic "Irreducible holomorphic symplectic manifolds"

1

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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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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"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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