Geometry & Topology Volume 23, issue 7 (2019)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author index

To appear

Other MSP journals

Moduli of stable maps in genus one and logarithmic geometry, I

Dhruv Ranganathan, Keli Santos-Parker and Jonathan Wise

Geometry & Topology 23 (2019) 3315–3366

DOI: 10.2140/gt.2019.23.3315

Bibliography

1	D Abramovich, C Cadman, B Fantechi, J Wise, Expanded degenerations and pairs, Comm. Algebra 41 (2013) 2346 MR3225278
2	D Abramovich, B Hassett, Stable varieties with a twist, from: "Classification of algebraic varieties" (editors C Faber, G van der Geer, E Looijenga), Eur. Math. Soc. (2011) 1 MR2742569
3	M Artin, Théorème de changement de base pour un morphisme propre, from: "Théorie des topos et cohomologie étale des schémas, Tome 3 (SGA 4₃ )" (editors M Artin, A Grothendieck, J L Verdier), Lecture Notes in Math. 305, Springer (1973) 79 MR0354654
4	P Belmans, A J de Jong, others, The Stacks project, electronic reference (2017)
5	R Cavalieri, M Chan, M Ulirsch, J Wise, A moduli stack of tropical curves, preprint (2017) arXiv:1704.03806
6	I Ciocan-Fontanine, B Kim, Moduli stacks of stable toric quasimaps, Adv. Math. 225 (2010) 3022 MR2729000
7	Y Cooper, The geometry of stable quotients in genus one, Math. Ann. 361 (2015) 943 MR3319554
8	T Foster, D Ranganathan, M Talpo, M Ulirsch, Logarithmic Picard groups, chip firing, and the combinatorial rank, Math. Z. 291 (2019) 313 MR3936072
9	M Gross, B Siebert, Logarithmic Gromov–Witten invariants, J. Amer. Math. Soc. 26 (2013) 451 MR3011419
10	A Grothendieck, Eléments de géométrie algébrique, IV : Étude locale des schémas et des morphismes de schémas, I, Inst. Hautes Études Sci. Publ. Math. 20 (1964) 5 MR173675
11	A Grothendieck, Eléments de géométrie algébrique, IV : Étude locale des schémas et des morphismes de schémas, II, Inst. Hautes Études Sci. Publ. Math. 24 (1965) 5 MR0199181
12	A Grothendieck, Techniques de construction et théorèmes d’existence en géométrie algébrique, IV : Les schémas de Hilbert, from: "Séminaire Bourbaki 1960∕1961", W A Benjamin (1966) 249 MR1611822
13	J Hall, D Rydh, Coherent Tannaka duality and algebraicity of Hom-stacks, Algebra Number Theory 13 (2019) 1633 MR4009673
14	R Hartshorne, Algebraic geometry, 52, Springer (1977) MR0463157
15	D Holmes, Néron models of jacobians over base schemes of dimension greater than 1, J. Reine Angew. Math. 747 (2019) 109 MR3905131
16	Y Hu, J Li, Genus-one stable maps, local equations, and Vakil–Zinger’s desingularization, Math. Ann. 348 (2010) 929 MR2721647
17	T Kajiwara, Logarithmic compactifications of the generalized Jacobian variety, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 40 (1993) 473 MR1255052
18	F Kato, Exactness, integrality, and log modifications, preprint (1999) arXiv:math/9907124
19	F Kato, Log smooth deformation and moduli of log smooth curves, Internat. J. Math. 11 (2000) 215 MR1754621
20	B Kim, Logarithmic stable maps, from: "New developments in algebraic geometry, integrable systems and mirror symmetry" (editors M H Saito, S Hosono, K Yoshioka), Adv. Stud. Pure Math. 59, Math. Soc. Japan (2010) 167 MR2683209
21	S L Kleiman, Relative duality for quasicoherent sheaves, Compositio Math. 41 (1980) 39 MR578050
22	J Kollár, S Mori, Birational geometry of algebraic varieties, 134, Cambridge Univ. Press (1998) MR1658959
23	R Lazarsfeld, Positivity in algebraic geometry, I : Classical setting — line bundles and linear series, 48, Springer (2004) MR2095471
24	C Manolache, Virtual pull-backs, J. Algebraic Geom. 21 (2012) 201 MR2877433
25	A Marian, D Oprea, R Pandharipande, The moduli space of stable quotients, Geom. Topol. 15 (2011) 1651 MR2851074
26	D Mumford, Abelian varieties, 5, Hindustan (1974) MR2514037
27	B Parker, Exploded manifolds, Adv. Math. 229 (2012) 3256 MR2900440
28	K S Parker, Semistable modular compactifications of moduli spaces of genus one curves, PhD thesis, University of Colorado at Boulder (2017) MR3697678
29	D Ranganathan, K Santos-Parker, J Wise, Moduli of stable maps in genus one and logarithmic geometry, II, Algebra Number Theory 13 (2019) 1765 MR4017534
30	D I Smyth, Modular compactifications of the space of pointed elliptic curves, I, Compos. Math. 147 (2011) 877 MR2801404
31	R Vakil, The enumerative geometry of rational and elliptic curves in projective space, J. Reine Angew. Math. 529 (2000) 101 MR1799935
32	R Vakil, A Zinger, A natural smooth compactification of the space of elliptic curves in projective space, Electron. Res. Announc. Amer. Math. Soc. 13 (2007) 53 MR2320682
33	R Vakil, A Zinger, A desingularization of the main component of the moduli space of genus-one stable maps into ℙⁿ, Geom. Topol. 12 (2008) 1 MR2377245
34	M Viscardi, Alternate compactifications of the moduli space of genus one maps, Manuscripta Math. 139 (2012) 201 MR2959678
35	A Zinger, The reduced genus 1 Gromov–Witten invariants of Calabi–Yau hypersurfaces, J. Amer. Math. Soc. 22 (2009) 691 MR2505298
36	A Zinger, A sharp compactness theorem for genus-one pseudo-holomorphic maps, Geom. Topol. 13 (2009) 2427 MR2529940