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References (42)
-
V. Batyrev, Y. Manin (1990)
Sur le nombre des points rationnels de hauteur borné des variétés algébriquesMathematische Annalen, 286
-
Eric Riedl, David Yang (2014)
Kontsevich spaces of rational curves on Fano hypersurfacesJournal für die reine und angewandte Mathematik (Crelles Journal)
-
S Mori (1982)
10.2307/2007050Ann. Math., 116
-
S. Mori (1980)
Threefolds whose canonical bundles are not numerically effective.Proceedings of the National Academy of Sciences of the United States of America, 77 6
-
10.1007/978-3-662-03276-3
-
M. Shen (2012)
On the normal bundles of rational curves on Fano 3-foldsAsian Journal of Mathematics, 16
-
Emmanuel Peyre (1995)
HAUTEURS ET MESURES DE TAMAGAWA SUR LES VARIÉTÉS DE FANODuke Mathematical Journal, 79
-
A. Iliev, L. Manivel (2005)
Pfaffian Lines and Vector Bundles on Fano Threefolds of Genus 8Journal of Algebraic Geometry, 16
-
(1910)
Lines, conics, and all that (2019) -
J. Franke, Y. Manin, Y. Tschinkel (1989)
Rational points of bounded height on Fano varietiesInventiones mathematicae, 95
-
Christopher Hacon, Chen Jiang (2016)
On Fujita invariants of subvarieties of a uniruled varietyarXiv: Algebraic Geometry
-
A. Grothendieck (1961)
Techniques de construction et théorèmes d'existence en géométrie algébrique IV : les schémas de Hilbert, 6
-
J. Kollár, Y. Miyaoka, S. Mori (1992)
Rational connectedness and bound-edness of Fano manifolds -
T. Browning, P. Vishe (2016)
Rational curves on smooth hypersurfaces of low degreearXiv: Algebraic Geometry
-
Classification problems andmirror duality -
V. Batyrev, Y. Tschinkel (1997)
Tamagawa numbers of polarized algebraic varietiesAstérisque
-
VA Iskovskih (1977)
10.1070/IM1977v011n03ABEH001733I. Math. USSR-Izv., 11
-
V. Iskovskikh (1980)
Anticanonical models of three-dimensional algebraic varietiesJournal of Soviet Mathematics, 13
-
Y. Miyaoka (1995)
Rational Curves on Algebraic Varieties -
Brian Lehmann, Sho Tanimoto (2017)
Geometric Manin’s conjecture and rational curvesCompositio Mathematica, 155
-
B. Hassett, Sho Tanimoto, Y. Tschinkel (2013)
Balanced line bundles and equivariant compactifications of homogeneous spacesInternational Mathematics Research Notices, 2015
-
VA Iskovskih (1978)
10.1070/IM1978v012n03ABEH001994II. Math. USSR-Izv., 12
-
Joe Harris, Mike Roth, Jason Starr (2002)
Rational curves on hypersurfaces of low degreeCrelle's Journal, 2004
-
Brian Lehmann, Sho Tanimoto (2018)
Rational curves on prime Fano threefolds of index 1Journal of Algebraic Geometry
-
Roya Beheshti, N. Kumar (2011)
Spaces of rational curves on complete intersectionsCompositio Mathematica, 149
-
C. Voisin, Leila Schneps (2002)
Hodge Theory and Complex Algebraic Geometry I: The Hodge Decomposition -
Brian Lehmann, A. Sengupta, Sho Tanimoto (2018)
Geometric consistency of Manin's conjectureCompositio Mathematica, 158
-
A. Höring (2010)
The sectional genus of quasi-polarised varietiesArchiv der Mathematik, 95
-
Scientifiques L’É.N.S, F. Campana, Par Campana (1992)
Connexité rationnelle des variétés de FanoAnnales Scientifiques De L Ecole Normale Superieure, 25
-
J Harris, M Roth, J Starr (2004)
Rational curves on hypersurfaces of low degreeJ. Reine Angew. Math., 571
-
Ana-Maria Castravet (2003)
Rational families of vector bundles on curves, IIarXiv: Algebraic Geometry
-
Brian Lehmann, Sho Tanimoto (2016)
On the geometry of thin exceptional sets in Manin's ConjecturearXiv: Algebraic Geometry
-
Brian Lehmann, Sho Tanimoto (2019)
Classifying sections of del Pezzo fibrations, IJournal of the European Mathematical Society
-
S. Boucksom, J. Demailly, Mihai Paun, T. Peternell (2004)
The pseudo-effective cone of a compact K\ -
A. Tihomirov (1982)
The Fano Surface of the Veronese Double ConeMathematics of The Ussr-izvestiya, 19
-
Emmanuel Peyre (2003)
Points de hauteur bornée, topologie adélique et mesures de TamagawaJournal de Theorie des Nombres de Bordeaux, 15
-
Roya Beheshti, Brian Lehmann, Eric Riedl, Sho Tanimoto (2021)
Rational curves on del Pezzo surfaces in positive characteristicTransactions of the American Mathematical Society, Series B
-
K. Behrend, Y. Manin (1995)
Stacks of Stable Maps and Gromov-Witten InvariantsDuke Mathematical Journal, 85
-
Izzet Coskun, J. Starr (2009)
Rational Curves on Smooth Cubic HypersurfacesInternational Mathematics Research Notices, 2009
-
Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations -
VV Golyshev (2007)
10.1017/CBO9780511721472.004 -
10.1007/s40879-021-00516-2
- Publisher
- Springer Journals
- Copyright
- Copyright © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021
- ISSN
- 2199-675X
- eISSN
- 2199-6768
- DOI
- 10.1007/s40879-021-00516-2
- Publisher site
- See Article on Publisher Site
Abstract
We prove the irreducibility of moduli spaces of rational curves on a general del Pezzo threefold of Picard rank 1 and degree 1. As corollaries, we confirm Geometric Manin’s conjecture and enumerativity of certain Gromov–Witten invariants for these threefolds.
Journal
European Journal of Mathematics – Springer Journals
Published: Mar 1, 2022
Keywords: Rational curves; Moduli spaces; Fano varieties; 14H10; 14J45