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On some families of Gushel-Mukai fourfolds. (English) Zbl 1507.14060

Summary: We give explicit descriptions of some Noether-Lefschetz divisors in the moduli space of Gushel-Mukai fourfolds. As a consequence we obtain that their Kodaira dimension is negative.

MSC:

14J35 \(4\)-folds
14J45 Fano varieties
14Q10 Computational aspects of algebraic surfaces
68W30 Symbolic computation and algebraic computation
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References:

[1] 10.14231/ag-2018-002 · Zbl 1408.14053 · doi:10.14231/ag-2018-002
[2] 10.1215/21562261-2019-0030 · Zbl 1440.14053 · doi:10.1215/21562261-2019-0030
[3] 10.1142/S0129167X20500135 · Zbl 1467.14031 · doi:10.1142/S0129167X20500135
[4] 10.1017/CBO9781107416000.009 · Zbl 1326.14094 · doi:10.1017/CBO9781107416000.009
[5] 10.1007/978-3-662-04851-1 · Zbl 0973.00017 · doi:10.1007/978-3-662-04851-1
[6] 10.1007/s00208-020-02036-y · Zbl 1492.14061 · doi:10.1007/s00208-020-02036-y
[7] ; Gushel, N. P., Fano varieties of genus 6, Izv. Akad. Nauk SSSR Ser. Mat., 46, 6, 1159 (1982) · Zbl 0554.14014
[8] ; Hassett, Brendan, Some rational cubic fourfolds, J. Algebraic Geom., 8, 1, 103 (1999) · Zbl 0961.14029
[9] 10.1023/A:1001706324425 · Zbl 0956.14031 · doi:10.1023/A:1001706324425
[10] 10.1007/978-3-319-46209-7_2 · Zbl 1454.14111 · doi:10.1007/978-3-319-46209-7_2
[11] 10.1007/s00209-020-02498-5 · Zbl 1450.14006 · doi:10.1007/s00209-020-02498-5
[12] 10.2140/jsag.2015.7.31 · Zbl 1422.14017 · doi:10.2140/jsag.2015.7.31
[13] 10.2140/ant.2017.11.1597 · Zbl 1375.14054 · doi:10.2140/ant.2017.11.1597
[14] 10.1073/pnas.86.9.3000 · Zbl 0679.14020 · doi:10.1073/pnas.86.9.3000
[15] 10.14231/AG-2017-015 · Zbl 1386.14024 · doi:10.14231/AG-2017-015
[16] ; Ottaviani, Giorgio, On 3-folds in ℙ5 which are scrolls, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 19, 3, 451 (1992) · Zbl 0786.14026
[17] 10.1007/BF02413916 · Zbl 0036.22502 · doi:10.1007/BF02413916
[18] 10.1215/00127094-2018-0053 · Zbl 1442.14051 · doi:10.1215/00127094-2018-0053
[19] 10.1007/978-3-030-75421-1_12 · Zbl 1497.14028 · doi:10.1007/978-3-030-75421-1\_12
[20] 10.4171/JEMS/1248 · Zbl 1521.14032 · doi:10.4171/JEMS/1248
[21] ; Schreyer, Frank-Olaf, Computer aided unirationality proofs of moduli spaces, Handbook of moduli, III. Adv. Lect. Math., 26, 257 (2013) · Zbl 1322.14021
[22] 10.2140/jsag.2018.8.61 · Zbl 1408.14050 · doi:10.2140/jsag.2018.8.61
[23] 10.2140/jsag.2018.8.21 · Zbl 1409.13052 · doi:10.2140/jsag.2018.8.21
[24] 10.2140/jsag.2021.11.143 · Zbl 1485.14026 · doi:10.2140/jsag.2021.11.143
[25] 10.1007/s00009-021-01797-3 · Zbl 1473.14078 · doi:10.1007/s00009-021-01797-3
[26] 10.1515/crelle-2016-0053 · Zbl 1439.14118 · doi:10.1515/crelle-2016-0053
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