Geometry & Topology Volume 28, issue 1 (2024)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

The desingularization of the theta divisor of a cubic threefold as a moduli space

Arend Bayer, Sjoerd Viktor Beentjes, Soheyla Feyzbakhsh, Georg Hein, Diletta Martinelli, Fatemeh Rezaee and Benjamin Schmidt

Geometry & Topology 28 (2024) 127–160

DOI: 10.2140/gt.2024.28.127

Bibliography

1	M Altavilla, M Petković, F Rota, Moduli spaces on the Kuznetsov component of Fano threefolds of index 2, Épijournal Géom. Algébrique 6 (2022) 13 MR4482373
2	D Arcara, A Bertram, Bridgeland-stable moduli spaces for K–trivial surfaces, J. Eur. Math. Soc. 15 (2013) 1 MR2998828
3	M Artebani, R Kloosterman, M Pacini, A new model for the theta divisor of the cubic threefold, Matematiche (Catania) 58 (2003) 201 MR2216132
4	M Artin, Algebraization of formal moduli, II : Existence of modifications, Ann. of Math. 91 (1970) 88 MR0260747
5	A Bayer, M Lahoz, E Macrì, P Stellari, Stability conditions on Kuznetsov components, Ann. Sci. Éc. Norm. Supér. 56 (2023) 517 MR4598728
6	A Bayer, E Macrì, P Stellari, The space of stability conditions on abelian threefolds, and on some Calabi–Yau threefolds, Invent. Math. 206 (2016) 869 MR3573975
7	A Bayer, E Macrì, Y Toda, Bridgeland stability conditions on threefolds, I : Bogomolov–Gieseker type inequalities, J. Algebraic Geom. 23 (2014) 117 MR3121850
8	A Beauville, Les singularités du diviseur Θ de la Jacobienne intermédiaire de l’hypersurface cubique dans ℙ⁴, from: "Algebraic threefolds" (editor A Conte), Lecture Notes in Math. 947, Springer (1982) 190 MR0672617
9	A Beauville, Vector bundles on the cubic threefold, from: "Symposium in honor of C H Clemens" (editors A Bertram, J A Carlson, H Kley), Contemp. Math. 312, Amer. Math. Soc. (2002) 71 MR1941574
10	P Belmans, A J de Jong, others, The Stacks project, electronic reference (2005–)
11	M Bernardara, E Macrì, S Mehrotra, P Stellari, A categorical invariant for cubic threefolds, Adv. Math. 229 (2012) 770 MR2855078
12	T Bridgeland, Stability conditions on triangulated categories, Ann. of Math. 166 (2007) 317 MR2373143
13	T Bridgeland, Stability conditions on K3 surfaces, Duke Math. J. 141 (2008) 241 MR2376815
14	C H Clemens, P A Griffiths, The intermediate Jacobian of the cubic threefold, Ann. of Math. 95 (1972) 281 MR0302652
15	I Coskun, J Huizenga, The ample cone of moduli spaces of sheaves on the plane, Algebr. Geom. 3 (2016) 106 MR3455422
16	L Ein, R Lazarsfeld, Singularities of theta divisors and the birational geometry of irregular varieties, J. Amer. Math. Soc. 10 (1997) 243 MR1396893
17	S Feyzbakhsh, L Pertusi, Serre-invariant stability conditions and Ulrich bundles on cubic threefolds, Épijournal Géom. Algébrique 7 (2023) 1 MR4545360
18	D Gieseker, On the moduli of vector bundles on an algebraic surface, Ann. of Math. 106 (1977) 45 MR0466475
19	P A Griffiths, Periods of integrals on algebraic manifolds, II : Local study of the period mapping, Amer. J. Math. 90 (1968) 805 MR0233825
20	D Happel, I Reiten, S O Smalø, Tilting in abelian categories and quasitilted algebras, 575, Amer. Math. Soc. (1996) MR1327209
21	R Hartshorne, Algebraic geometry, 52, Springer (1977) MR0463157
22	R Hartshorne, Generalized divisors on Gorenstein schemes, K–Theory 8 (1994) 287 MR1291023
23	D Huybrechts, M Lehn, The geometry of moduli spaces of sheaves, Cambridge Univ. Press (2010) MR2665168
24	A Iliev, Minimal sections of conic bundles, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. 2 (1999) 401 MR1706556
25	A G Kuznetsov, Derived category of a cubic threefold and the variety V ₁₄, Tr. Mat. Inst. Steklova 246 (2004) 183 MR2101293
26	C Li, Stability conditions on Fano threefolds of Picard number 1, J. Eur. Math. Soc. 21 (2019) 709 MR3908763
27	J Lo, Y More, Some examples of tilt-stable objects on threefolds, Comm. Algebra 44 (2016) 1280 MR3463144
28	A Maciocia, Computing the walls associated to Bridgeland stability conditions on projective surfaces, Asian J. Math. 18 (2014) 263 MR3217637
29	E Macrì, B Schmidt, Derived categories and the genus of space curves, Algebr. Geom. 7 (2020) 153 MR4061326
30	M Maruyama, Moduli of stable sheaves. I, J. Math. Kyoto Univ. 17 (1977) 91 MR0450271
31	M Maruyama, Moduli of stable sheaves. II, J. Math. Kyoto Univ. 18 (1978) 557 MR0509499
32	D Mumford, Projective invariants of projective structures and applications, from: "Proceedings of the International Congress of Mathematicians" (editor V Stenström), Institut Mittag-Leffler (1963) 526 MR0175899
33	D Mumford, Prym varieties, I, from: "Contributions to analysis : a collection of papers dedicated to Lipman Bers" (editors L V Ahlfors, I Kra, B Maskit, L Nirenberg), Academic (1974) 325 MR0379510
34	A Perry, The integral Hodge conjecture for two-dimensional Calabi–Yau categories, Compos. Math. 158 (2022) 287 MR4406785
35	L Pertusi, S Yang, Some remarks on Fano threefolds of index two and stability conditions, Int. Math. Res. Not. 2022 (2022) 12940 MR4475280
36	K Schwede, Generalized divisors and reflexive sheaves, lecture notes (2007)
37	C T Simpson, Moduli of representations of the fundamental group of a smooth projective variety, I, Inst. Hautes Études Sci. Publ. Math. 79 (1994) 47 MR1307297
38	F Takemoto, Stable vector bundles on algebraic surfaces, Nagoya Math. J. 47 (1972) 29 MR0337966
39	G E Welters, Abel–Jacobi isogenies for certain types of Fano threefolds, 141, Mathematisch Centrum (1981) MR0633157
40	S Zhang, Bridgeland moduli spaces for Gushel–Mukai threefolds and Kuznetsov’s Fano threefold conjecture, preprint (2021) arXiv:2012.12193v2