Диссертация (Числа Бетти и трианалитические подмногообразия гиперкэлеровых многообразий), страница 11
Описание файла
Файл "Диссертация" внутри архива находится в папке "Числа Бетти и трианалитические подмногообразия гиперкэлеровых многообразий". PDF-файл из архива "Числа Бетти и трианалитические подмногообразия гиперкэлеровых многообразий", который расположен в категории "". Всё это находится в предмете "физико-математические науки" из Аспирантура и докторантура, которые можно найти в файловом архиве НИУ ВШЭ. Не смотря на прямую связь этого архива с НИУ ВШЭ, его также можно найти и в других разделах. , а ещё этот архив представляет собой кандидатскую диссертацию, поэтому ещё представлен в разделе всех диссертаций на соискание учёной степени кандидата физико-математических наук.
Просмотр PDF-файла онлайн
Текст 11 страницы из PDF
Preprint arXiv:1511.02838v2 [math.AG].[Ku4] Курносов Н.М., Доклад “Absolutely trianalytic tori in the generalized Kummervariety” , V Школа-конференция по алгебраической геометрии и комплексному анализу для молодых математиков России, Коряжма, 17-22.08.2015.[Ku5] Курносов Н.М., Доклад “Ограничения на когомологии гиперкэлеровых многообразий” , VI Международная конференция по алгебраической геометрии, комплексному анализу и компьютерной алгебре, Коряжма, 03-09.08.2016.74Список литературы[AL] Addington N., Lehn M., On the symplectic eightfold associated to a Pfaffian cubicfourfold.
Preprint arXiv:1404.5657v2 [math.AG].[B] Bogomolov F.A., On the decomposition of Kähler manifolds with trivial canonical class,Math. USSR-Sb. 22, pp. 580 - 583, 1974.[B2] Bogomolov F.A., On Guan’s example of simply connected non-Kahler compact complexmanifolds, Am. J. Math., 118 , pp. 1037-1046, 1996.[Bea1] Beauville A., Holomorphic symplectic geometry: a problem list.
Preprint,arXiv:1002.4321v1 [math.AG].[Bea2] Beauville A., Varietes Kahleriennes dont la premi‘ere classe de Chern est nulle, J.Diff. Geom., 18, pp. 755-782, 1983.[BD] Beauville, A., Donagi, R., La variété des droites d’une hypersurface cubique dedimension 4. C. R. Acad. Sci. Paris Sér. I Math., 301, 14, pp.
703–706, 1985.[Ber] Berger, M. Classification des espaces homogenes symétriques irreductibles., C. r. Acad.sci. Paris, 240, pp. 2370-2372, 1985.[Bes] Besse A., Einstein Manifolds, Springer-Verlag, New York, 1987.[BNS] Boissiere S., Nieper-Wisskirchen M., Sarti A., Higher dimensional Enriques varietiesand automorphisms of generalized Kummer varieties, Journal de Mathematiques Pureset Appliquees, vol. 95, 5, pp. 553-563, 2011. Preprint arXiv:1001.4728v3 [math.AG].[Del] Deligne, P., Hodge cycles on abelian varieties (notes by J.
S. Milne), in Lecture Notesin Mathematics, 900 (1982), pp. 9-100, Springer- Verlag.[DHM] Dadok J., Harvey R., Morgan F., Calibrations in R8 , Trans. Amer Math. Soc., 307,pp. 1-40, 1988.[EPW] Eisenbud D., Popescu S., Walter Ch., Lagrangian subbundles and codimension 3subcanonical sub- schemes., Duke Math. J., 107, 3, pp. 427–467, 2001.[EV] Entov M., Verbitsky M., Full symplectic packing for tori and hyperkahler manifolds.Preprint arXiv:1412.7183 [math.AG].[F] Fujiki A., On the de Rham cohomology group of a compact Kähler symplectic manifold,Adv. St.
Pure Math, 10, pp. 105-165, 1987.[GH] Griffiths P., Harris J., Principles of Algebraic Geometry, John Wiley & Sons, Inc. 1978.[GHJ] Gross M., Huybrechts D., Joyce D., Calabi-Yau Manifolds and Related Geometries,Lectures at a Summer School in Nordfjordeid, 2003.[GK] Ginzburg V., Kaledin D., Poisson deformations of symplectic quotient singularities,Adv.
Math., 186, no. 1, 1-57, 2004.[GS] Göttsche L., Soergel W., Perverse sheaves and the cohomology of Hilbert schemes ofsmooth algebraic surfaces, Math. Ann., 296, 1, 235-245.[GrH] Gritsenko V., Hirzebruch F., On the Euler characteristic of manifolds with 1 = 0. Aletter to V. Gritsenko., Algebra and Analysis, 11 (5).
pp. 126-129, 1999.[GV] Grantcharov G., Verbitsky M., Calibrations in hyperkähler geometry. Calibrationsin hyperkähler geometry, Commun. Contemp. Math., 15, 1250060, 2013. PreprintarXiv:1009.1178 [math.AG].[Gu] Guan G., On the Betti numbers of irreducible compact hyperkähler manifolds of complexdimension four, Math. Res. Lett., 8, 5-6, pp 663-669, 2001.[Gu2] Guan D., On representation theory and the cohomology rings of irreducible compacthyperkähler manifolds of complex dimension four, Cent. Eur. J.
of Math., 1, 4, pp661–669, 2003.[Gu3] Guan, D., Examples of compact holomorphic symplectic manifolds which are notKahlerian. II, Invent. Math., 121, 1, pp. 135–145, 200575[H1] Huybrechts D., Finiteness results for hyperkähler manifolds, preprint arXiv:0109024[math.AG].[H2] Huybrechts D., Compact Hyperkähler Manifolds. In book M.
Gross, D. Huybrechts, andD. Joyce, Calabi-Yau manifolds and related geometries, Springer Universitext, 2002.[HL] Huybrechts D., Lehn M., The Geometry of Moduli Spaces of Sheaves, Aspects ofMathematics, E. 31, Vieweg Verlag (1997).[HarL] Harvey R., Lawson B., Calibrated geometries, Acta Math., 148, pp. 47-157, 1982.[HS] Hitchin N., Sawon J.„ Curvature and Characteristic Numbers of Hyperkähler Manifolds,Duke Math. J., 106(3), pp. 599-615, 2001. Preprint version, arXiv:math/9908114v1[J] Joyce D., Compact manifolds with special holonomy, Oxford Mathematical MonographsSeries, Oxford University Press, 2000[K] Kaledin D., Symplectic singularities from the Poisson point of view, Journal für diereine und angewandte Mathematik (Crelles Journal), 600, pp.
135–156, 2006. PreprintarXiv:0310186v4 [math.AG].[Ka] Kapustka G., On IHS fourfolds with 2 = 23, preprint arXiv:1403.1074 [math.AG].[Kam] Kamenova L., Finiteness of Lagrangian fibrations with fixed invariants, ComptesRendus Mathematique, 354, 7, pp. 707–711, 2016. Preprint arXiv:1509.01897[math.AG].[Kap] Kapfer S., Computing Cup-Products in integral cohomology of Hilbert schemes of pointson K3 surfaces, LMS Jour. Comp. Math., 19, pp. 78-97, 2006.[Kapr] Kapranov M., Rozansky-Witten invariants via Atiyah classes, Compositio Math, 115,pp. 71-113, 1999.[KM] Kollar J., Matsusaka T., Riemann-Roch Type Inequalities, American Journal ofMathematics, 105, 1, pp. 229-252, 1983.[KLS] Kaledin D., Lehn M., Sorger C., Singular symplectic moduli spaces, Invent. Math.,164, no.
3, pp. 591–614, 2006.[KoS] Kotschick D., Schreieder S., The Hodge ring of Kaehler manifolds, Compositio Math.,149, pp. 637-657, 2013. Preprint arXiv:0504202 [math.AG].[KV] Kaledin D., Verbitsky M., Trianalytic subvarieties of generalized Kummer varieties,Internat. Math. Res. Notices, 9, pp. 439–461, 1998. Preprint arXiv:9801038 [math.AG].[KV1] Kaledin D., Verbitsky M., Partial resolutions of Hilbert type, Dynkin diagrams, andgeneralized Kummer varieties.
Preprint arXiv:9812078 [math.AG].[KV-book] Kaledin D., Verbitsky M., Hyperkähler manifolds, International Press, Boston,2001.[LL] Looijenga E., Lunts V., A Lie algebra attached to a projective variety, Invent. math.,129, pp. 361-412, 1997.[LS] Lehn M., Sorger C., The cup product of Hilbert schemes for K3 surfaces, Invent. math.,152, 2, pp 305–329, 2003.[LLSV] Lehn C., Lehn M., Sorger C., van Straten D., Twisted cubics on cubic fourfoldsJournal für die reine und angewandte Mathematik, DOI: 10.1515/crelle-2014-0144,2015.[MRS] Mongardi G., Rapagnetta A., Saccà G., The Hodge diamond of O’Grady’s6-dimensional example.
Preprint arXiv:1603.06731 [math.AG].[Ma] Markman E., Integral constraints on the monodromy group of the hyperkahler resolutionof a symmetric product of a 3 surface, Int. Journ. of Math., 21, 2, pp. 169-223, 2010.[Mo] Mozgovoy S., The Euler number of O’Grady’s ten-dimensional symplectic manifold,PhD thesis University of Mainz, 2006.[Mu] Mukai S., On the moduli space of bundles on 3 surfaces I, Vector Bundles on AlgebraicVarieties, TIFR, Bombay, O.U.P. (1987), pp. 341-413.76[MW] Mongardi G., Wandel M., Automorphisms of O’Grady’s Manifolds Acting Trivially onCohomology, Preprint arXiv:1411.0759 [math.AG].[N] Nakajima H., Lectures on Hilbert Schemes of Points on Surfaces, University LectureSeries, 1999.[N-W] Nieper-Weisskirchen M., Hirzebruch-Riemann-Roch Formulae on IrreducibleSymplectic Kähler Manifolds, J. Algebraic Geom., 12, 4, pp.
715-739., 2003.[O1] O’Grady K.G., Desingularized moduli spaces of sheaves on a 3, J. fur die reine undangew. Math., 512, pp. 49-117, 1999. Preprint arXiv:9708009v2 [math.AG].[O2] O’Grady K.G., A new six-dimensional irreducible symplectic variety, J. AlgebraicGeom., 12, pp. 435-505, 2003.[O3] O’Grady K.G., The weight-two Hodge structure of moduli spaces of sheaves on a 3surface, J. of Alg. Geom., 6, pp.
599-644, 1997.[Og] Oguiso K., No cohomologically trivial non-trivial automorphism of generalized Kummermanifolds, Preprint arXiv:1208.3750v3 [math.AG].[OVV] Ornea L., Verbitsky M., Vuletescu V., Blow-ups of LCK manifold, Int. Math. Res.Not., 12, pp.
2809-2821, 2013. Preprint arXiv:1108.4885v2 [math.AG].[R] Rapagnetta A., Topological invariants of O’Grady’s six dimensional irreduciblesymplectic variety, Math. Z., 256, pp. 1-34, 2007. Preprint arXiv:0406026v2 [math.AG].[RW] Rozansky L., Witten E., Hyperkähler geometry and invariants of three- manifolds,Selecta Mathematica (N.S., 3, pp. 401-458, 1997.[S] Sawon J., Rozansky-Witten Invariants of Hyperkähler Manifolds, PhD thesis Universityof Cambridge, 1999.[S-b2] Sawon J., A bound on the second Betti number of hyperkähler manifolds of complexdimension six, Preprint arXiv:1511.09105 [math.AG].[Sa] Salamon S., On the cohomology of Kähler and hyperkähler manifolds, Topology, 35,pp.
137-155, 1996.[Siu] Siu Y.-T., Every 3 surface is Kahler, Invent. math., 73 (1983), pp. 139-150.[SV] Soldatenkov A., Verbitsky M., k-symplectic structures and absolutely trianalyticsubvarieties, J. of Geometry and Physics, 92, pp. 147–156, 2015. PreprintarXiv:1409.1100v2 [math.AG].[V1] Verbitsky M., Hyperkähler and holomorphic symplectic geometry I, Journ.
of Alg.Geom., 5, no. 3, pp. 401-415, 1996. Preprint arXiv:9307009 [math.AG].[V2] Verbitsky M., Trianalytic subvarieties of hyperkaehler manifolds, GAFA, 5, no. 1, pp.92-104, 1995. Preprint arXiv:9403006 [math.AG].[V3] Verbitsky M., Trianalytic subvarieties of the Hilbert scheme of points on a 3 surface,GAFA, 8, pp. 732-782, 1998.