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K3 surfaces associated with varieties of generalized Kummer type

Salvatore Floccari

Geometry & Topology 30 (2026) 1129–1154
Bibliography
1 N Addington, On two rationality conjectures for cubic fourfolds, Math. Res. Lett. 23 (2016) 1 MR3512874
2 G Ancona, M Cavicchi, R Laterveer, G Saccà, Relative and absolute Lefschetz standard conjectures for some Lagrangian fibrations, J. Lond. Math. Soc. (2) 111 (2025) MR4888342
3 Y André, On the Shafarevich and Tate conjectures for hyper-Kähler varieties, Math. Ann. 305 (1996) 205 MR1391213
4 Y André, Pour une théorie inconditionnelle des motifs, Inst. Hautes Études Sci. Publ. Math. (1996) 5 MR1423019
5 Y André, Une introduction aux motifs (motifs purs, motifs mixtes, périodes), 17, Soc. Math. France (2004) MR2115000
6 D Arapura, Motivation for Hodge cycles, Adv. Math. 207 (2006) 762 MR2271985
7 A Bayer, E Macrì, MMP for moduli of sheaves on K3s via wall-crossing : nef and movable cones, Lagrangian fibrations, Invent. Math. 198 (2014) 505 MR3279532
8 A Bayer, E Macrì, Projectivity and birational geometry of Bridgeland moduli spaces, J. Amer. Math. Soc. 27 (2014) 707 MR3194493
9 A Beauville, Variétés Kähleriennes dont la première classe de Chern est nulle, J. Differential Geom. 18 (1983) 755 MR730926
10 S Boissière, M Nieper-Wißkirchen, A Sarti, Higher dimensional Enriques varieties and automorphisms of generalized Kummer varieties, J. Math. Pures Appl. (9) 95 (2011) 553 MR2786223
11 M Bolognesi, R Laterveer, A 9-dimensional family of K3 surfaces with finite-dimensional motive, Rend. Circ. Mat. Palermo (2) 73 (2024) 2313 MR4825006
12 J Briançon, Description de HilbnC{x,y}, Invent. Math. 41 (1977) 45 MR457432
13 T Bridgeland, Stability conditions on K3 surfaces, Duke Math. J. 141 (2008) 241 MR2376815
14 T H Bülles, Motives of moduli spaces on K3 surfaces and of special cubic fourfolds, Manuscripta Math. 161 (2020) 109 MR4046978
15 N Buskin, Every rational Hodge isometry between two K3 surfaces is algebraic, J. Reine Angew. Math. 755 (2019) 127 MR4015230
16 C Camere, Symplectic involutions of holomorphic symplectic four-folds, Bull. Lond. Math. Soc. 44 (2012) 687 MR2967237
17 F Charles, E Markman, The standard conjectures for holomorphic symplectic varieties deformation equivalent to Hilbert schemes of K3 surfaces, Compos. Math. 149 (2013) 481 MR3040747
18 P Deligne, La conjecture de Weil pour les surfaces K3, Invent. Math. 15 (1972) 206 MR296076
19 P Deligne, J S Milne, Tannakian categories, from: "Hodge cycles, motives, and Shimura varieties" (editors A Dold, B Eckmann), Lecture Notes in Mathematics 900, Springer (1982) 101 MR654325
20 S Floccari, The Hodge and Tate conjectures for hyper-Kähler sixfolds of generalized Kummer type, preprint (2023) arXiv:2308.02267
21 S Floccari, On the motive of O’Grady’s six-dimensional hyper-Kähler varieties, Épijournal Géom. Algébrique 7 (2023) 4 MR4582877
22 S Floccari, Sixfolds of generalized Kummer type and K3 surfaces, Compos. Math. 160 (2024) 388 MR4685665
23 S Floccari, M Varesco, Algebraic cycles on hyper-Kähler varieties of generalized Kummer type, Math. Ann. 391 (2025) 4443 MR4865246
24 S Floccari, L Fu, Z Zhang, On the motive of O’Grady’s ten-dimensional hyper-Kähler varieties, Commun. Contemp. Math. 23 (2021) 2050034 MR4237568
25 J Foster, The Lefschetz standard conjectures for IHSMs of generalized Kummer deformation type in certain degrees, Eur. J. Math. 10 (2024) 34 MR4751736
26 A Fujiki, On the de Rham cohomology group of a compact Kähler symplectic manifold, from: "Algebraic geometry" (editor T Oda), Adv. Stud. Pure Math. 10, North-Holland (1987) 105 MR946237
27 W Fulton, Intersection theory, 2, Springer (1998) MR1644323
28 B van Geemen, Kuga–Satake varieties and the Hodge conjecture, from: "The arithmetic and geometry of algebraic cycles" (editors B B Gordon, J D Lewis, S Müller-Stach, S Saito, N Yui), NATO Sci. Ser. C Math. Phys. Sci. 548, Kluwer (2000) 51 MR1744943
29 B van Geemen, Fourfolds of Weil type and the spinor map, Expo. Math. 41 (2023) 418 MR4602848
30 A Grothendieck, Standard conjectures on algebraic cycles, from: "Algebraic geometry" (editor S Abhyankar), Tata Inst. Fundam. Res. Stud. Math. 4, Tata Inst. Fund. Res. (1969) 193 MR268189
31 B Hassett, Y Tschinkel, Hodge theory and Lagrangian planes on generalized Kummer fourfolds, Mosc. Math. J. 13 (2013) 33, 189 MR3112215
32 D Huybrechts, Compact hyper-Kähler manifolds : basic results, Invent. Math. 135 (1999) 63 MR1664696
33 D Huybrechts, Lectures on K3 surfaces, 158, Cambridge Univ. Press (2016) MR3586372
34 D Huybrechts, Motives of isogenous K3 surfaces, Comment. Math. Helv. 94 (2019) 445 MR4014777
35 C Ingalls, A Logan, O Patashnick, Explicit coverings of families of elliptic surfaces by squares of curves, Math. Z. 302 (2022) 1191 MR4480228
36 U Jannsen, Motives, numerical equivalence, and semi-simplicity, Invent. Math. 107 (1992) 447 MR1150598
37 D Kaledin, M Verbitsky, Partial resolutions of Hilbert type, Dynkin diagrams, and generalized Kummer varieties, preprint (1998) arXiv:math/9812078
38 L Kamenova, G Mongardi, A Oblomkov, Symplectic involutions of K3[n] type and Kummer n type manifolds, Bull. Lond. Math. Soc. 54 (2022) 894 MR4453747
39 S L Kleiman, Algebraic cycles and the Weil conjectures, from: "Dix exposés sur la cohomologie des schémas" (editors A Grothendieck, N H Kuiper), Adv. Stud. Pure Math. 3, North-Holland (1968) 359 MR292838
40 M Kuga, I Satake, Abelian varieties attached to polarized K3-surfaces, Math. Ann. 169 (1967) 239 MR210717
41 E Markman, The monodromy of generalized Kummer varieties and algebraic cycles on their intermediate Jacobians, J. Eur. Math. Soc. (JEMS) 25 (2023) 231 MR4556784
42 J S Milne, The Tate and standard conjectures for certain abelian varieties, preprint (2021) arXiv:2112.12815
43 G Mongardi, M Wandel, Automorphisms of O’Grady’s manifolds acting trivially on cohomology, Algebr. Geom. 4 (2017) 104 MR3592467
44 B Moonen, Notes on Mumford–Tate groups, unpublished lecture notes (1999)
45 B J J Moonen, Y G Zarhin, Hodge classes and Tate classes on simple abelian fourfolds, Duke Math. J. 77 (1995) 553 MR1324634
46 D R Morrison, On K3 surfaces with large Picard number, Invent. Math. 75 (1984) 105 MR728142
47 D R Morrison, The Kuga–Satake variety of an abelian surface, J. Algebra 92 (1985) 454 MR778462
48 S Mukai, On the moduli space of bundles on K3 surfaces, I, from: "Vector bundles on algebraic varieties" (editor M F Atiyah), Tata Inst. Fund. Res. Stud. Math. 11, Tata Inst. Fund. Res. (1987) 341 MR893604
49 V V Nikulin, Kummer surfaces, Izv. Akad. Nauk SSSR Ser. Mat. 39 (1975) 278, 471 MR429917
50 K G O’Grady, The weight-two Hodge structure of moduli spaces of sheaves on a K3 surface, J. Algebraic Geom. 6 (1997) 599 MR1487228
51 K G O’Grady, Compact tori associated to hyperkähler manifolds of Kummer type, Int. Math. Res. Not. 2021 (2021) 12356 MR4300229
52 K Oguiso, No cohomologically trivial nontrivial automorphism of generalized Kummer manifolds, Nagoya Math. J. 239 (2020) 110 MR4138897
53 K Paranjape, Abelian varieties associated to certain K3 surfaces, Compositio Math. 68 (1988) 11 MR962501
54 M Varesco, Hodge similarities, algebraic classes, and Kuga–Satake varieties, Math. Z. 305 (2023) 69 MR4664576
55 M Varesco, The Hodge conjecture for powers of K3 surfaces of Picard number 16, Michigan Math. J. 75 (2025) 1085 MR4979927
56 M Verbitsky, Tri-analytic subvarieties of hyper-Kaehler manifolds, Geom. Funct. Anal. 5 (1995) 92 MR1312021
57 C Voisin, Footnotes to papers of O’Grady and Markman, Math. Z. 300 (2022) 3405 MR4395097
58 K Yoshioka, Moduli spaces of stable sheaves on abelian surfaces, Math. Ann. 321 (2001) 817 MR1872531