Academic literature on the topic 'Hilbert schemes of points on K3 surface'
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Journal articles on the topic "Hilbert schemes of points on K3 surface"
Charles, François, and Eyal Markman. "The standard conjectures for holomorphic symplectic varieties deformation equivalent to Hilbert schemes of K3 surfaces." Compositio Mathematica 149, no. 3 (February 7, 2013): 481–94. http://dx.doi.org/10.1112/s0010437x12000607.
Full textRyan, Tim, and Ruijie Yang. "Nef Cones of Nested Hilbert Schemes of Points on Surfaces." International Mathematics Research Notices 2020, no. 11 (May 28, 2018): 3260–94. http://dx.doi.org/10.1093/imrn/rny088.
Full textBruzzo, Ugo, and Antony Maciocia. "Hilbert schemes of points on some K3 surfaces and Gieseker stable bundles." Mathematical Proceedings of the Cambridge Philosophical Society 120, no. 2 (August 1996): 255–61. http://dx.doi.org/10.1017/s0305004100074843.
Full textCattaneo, Alberto. "Automorphisms of Hilbert schemes of points on a generic projective K3 surface." Mathematische Nachrichten 292, no. 10 (July 26, 2019): 2137–52. http://dx.doi.org/10.1002/mana.201800557.
Full textSawon, Justin. "Lagrangian fibrations on Hilbert schemes of points on K3 surfaces." Journal of Algebraic Geometry 16, no. 3 (September 1, 2007): 477–97. http://dx.doi.org/10.1090/s1056-3911-06-00453-x.
Full textKapfer, Simon. "Computing cup products in integral cohomology of Hilbert schemes of points on K3 surfaces." LMS Journal of Computation and Mathematics 19, no. 1 (2016): 78–97. http://dx.doi.org/10.1112/s1461157016000012.
Full textOberdieck, Georg. "Gromov–Witten invariants of the Hilbert schemes of points of a K3 surface." Geometry & Topology 22, no. 1 (October 31, 2017): 323–437. http://dx.doi.org/10.2140/gt.2018.22.323.
Full textBangere, Purnaprajna, Jayan Mukherjee, and Debaditya Raychaudhury. "K3 carpets on minimal rational surfaces and their smoothings." International Journal of Mathematics 32, no. 06 (April 7, 2021): 2150032. http://dx.doi.org/10.1142/s0129167x21500324.
Full textNeguţ, Andrei, Georg Oberdieck, and Qizheng Yin. "Motivic decompositions for the Hilbert scheme of points of a K3 surface." Journal für die reine und angewandte Mathematik (Crelles Journal) 2021, no. 778 (April 19, 2021): 65–95. http://dx.doi.org/10.1515/crelle-2021-0015.
Full textReede, Fabian, and Ziyu Zhang. "Stability of some vector bundles on Hilbert schemes of points on K3 surfaces." Mathematische Zeitschrift 301, no. 1 (December 3, 2021): 315–41. http://dx.doi.org/10.1007/s00209-021-02920-6.
Full textDissertations / Theses on the topic "Hilbert schemes of points on K3 surface"
CATTANEO, ALBERTO. "NON-SYMPLECTIC AUTOMORPHISMS OF IRREDUCIBLE HOLOMORPHIC SYMPLECTIC MANIFOLDS." Doctoral thesis, Università degli Studi di Milano, 2018. http://hdl.handle.net/2434/606455.
Full textWe study automorphisms of irreducible holomorphic symplectic manifolds of type K3^[n], i.e. manifolds which are deformation equivalent to the Hilbert scheme of n points on a K3 surface, for some n > 1. In the first part of the thesis we describe the automorphism group of the Hilbert scheme of n points on a generic projective K3 surface, i.e. a K3 surface whose Picard lattice is generated by a single ample line bundle. We show that, if it is not trivial, the automorphism group is generated by a non-symplectic involution, whose existence depends on some arithmetic conditions involving the number of points n and the polarization of the surface. We also determine necessary and sufficient conditions on the Picard lattice of the Hilbert scheme for the existence of the involution. In the second part of the thesis we study non-symplectic automorphisms of prime order on manifolds of type K3^[n]. We investigate the properties of the invariant lattice and its orthogonal complement inside the second cohomology lattice of the manifold, providing a classification of their isometry classes. We then approach the problem of constructing examples (or at least proving the existence) of manifolds of type K3^[n] with a non-symplectic automorphism inducing on cohomology each specific action in our classification. In the case of involutions, and of automorphisms of odd prime order for n=3,4, we are able to realize all possible cases. In order to do so, we present a new non-symplectic automorphism of order three on a ten-dimensional family of Lehn-Lehn-Sorger-van Straten eightfolds of type K3^[4]. Finally, for n < 6 we describe deformation families of large dimension of manifolds of type K3^[n] equipped with a non-symplectic involution.
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 géométriques pour l’existence de l’involution. Dans la deuxième partie, nous étudions les automorphismes non-symplectiques d’ordre premier des variétés de type K3^[n]. Nous déterminons les propriétés du réseau invariant de l'automorphisme et de son complément orthogonal dans le deuxième réseau de cohomologie de la variété et nous classifions leurs classes d’isométrie. Dans le cas des involutions, e des automorphismes d’ordre premier impair pour n = 3, 4, nous montrons que toutes les actions en cohomologie dans notre classification sont réalisées par un automorphism non-symplectique sur une variété de type K3^[n]. Nous construisons explicitement l’immense majorité de ces automorphismes et, en particulier, nous présentons la construction d’un nouvel automorphisme d’ordre trois sur une famille de dimension dix de variétés de Lehn-Lehn-Sorger-van Straten de type K3^[4]. Pour n < 6, nous étudions aussi les espaces de modules de dimension maximal des variétés de type K3^[n] munies d’une involution non-symplectique.
Cattaneo, Alberto. "Non-symplectic automorphisms of irreducible holomorphic symplectic manifolds." Thesis, Poitiers, 2018. http://www.theses.fr/2018POIT2322/document.
Full textWe study automorphisms of irreducible holomorphic symplectic manifolds of type K3^[n], i.e. manifolds which are deformation equivalent to the Hilbert scheme of n points on a K3 surface, for some n > 1. In the first part of the thesis we describe the automorphism group of the Hilbert scheme of n points on a generic projective K3 surface, i.e. a K3 surface whose Picard lattice is generated by a single ample line bundle. We show that, if it is not trivial, the automorphism group is generated by a non-symplectic involution, whose existence depends on some arithmetic conditions involving the number of points n and the polarization of the surface. We also determine necessary and sufficient conditions on the Picard lattice of the Hilbert scheme for the existence of the involution.In the second part of the thesis we study non-symplectic automorphisms of prime order on manifolds of type K3^[n]. We investigate the properties of the invariant lattice and its orthogonal complement inside the second cohomology lattice of the manifold, providing a classification of their isometry classes. We then approach the problem of constructing examples (or at least proving the existence) of manifolds of type K3^[n] with a non-symplectic automorphism inducing on cohomology each specific action in our classification. In the case of involutions, and of automorphisms of odd prime order for n=3,4, we are able to realize all possible cases. In order to do so, we present a new non-symplectic automorphism of order three on a ten-dimensional family of Lehn-Lehn-Sorger-van Straten eightfolds of type K3^[4]. Finally, for n < 6 we describe deformation families of large dimension of manifolds of type K3^[n] equipped with a non-symplectic involution
Tari, Kévin. "Automorphismes des variétés de Kummer généralisées." Thesis, Poitiers, 2015. http://www.theses.fr/2015POIT2301/document.
Full textLn this work, we classify non-symplectic automorphisms of varieties deformation equivalent to 4-dimensional generalized Kummer varieties, having a prime order action on the Beauville-Bogomolov lattice. Firstly, we give the fixed loci of natural automorphisms of this kind. Thereafter, we develop tools on lattices, in order to apply them to our varieties. A lattice-theoritic study of 2-dimensional complex tori allows a better understanding of natural automorphisms of Kummer-type varieties. Finaly, we classify all the automorphisms described above on thos varieties. As an application of our results on lattices, we complete also the classification of prime order automorphisms on varieties deformation-equivalent to Hilbert schemes of 2 points on K3 surfaces, solving the case of order 5 which was still open
Wandel, Malte [Verfasser]. "Stability of tautological bundles on Hilbert schemes of points on a surface / Malte Wandel." Hannover : Technische Informationsbibliothek und Universitätsbibliothek Hannover (TIB), 2013. http://d-nb.info/1043723609/34.
Full textArbesfeld, Noah. "K-theoretic enumerative geometry and the Hilbert scheme of points on a surface." Thesis, 2018. https://doi.org/10.7916/D8D80TK2.
Full textBooks on the topic "Hilbert schemes of points on K3 surface"
Huybrechts, D. Where to Go from Here. Oxford University Press, 2007. http://dx.doi.org/10.1093/acprof:oso/9780199296866.003.0013.
Full textBook chapters on the topic "Hilbert schemes of points on K3 surface"
Boissiére, Samuel, Andrea Cattaneo, Marc Nieper-Wisskirchen, and Alessandra Sarti. "The Automorphism Group of the Hilbert Scheme of Two Points on a Generic Projective K3 Surface." In K3 Surfaces and Their Moduli, 1–15. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-29959-4_1.
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