Enumeration of surfaces containing an elliptic quartic curve
A very general surface of degree at least four in ℙ3 contains no curves other than intersections with surfaces. We find a formula for the degree of the locus of surfaces in ℙ3 of degree at least five which contain some elliptic quartic curves. We also compute the degree of the locus of quartic surfa...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00029939_v142_n10_p3305_Cukierman |
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todo:paper_00029939_v142_n10_p3305_Cukierman2023-10-03T13:55:15Z Enumeration of surfaces containing an elliptic quartic curve Cukierman, F. Lopez, A.F. Vainsencher, I. Enumerative geometry Intersection theory Noether-Lefschetz locus A very general surface of degree at least four in ℙ3 contains no curves other than intersections with surfaces. We find a formula for the degree of the locus of surfaces in ℙ3 of degree at least five which contain some elliptic quartic curves. We also compute the degree of the locus of quartic surfaces containing an elliptic quartic curve, a case not covered by that formula. © 2014 American Mathematical Society. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00029939_v142_n10_p3305_Cukierman |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Enumerative geometry Intersection theory Noether-Lefschetz locus |
| spellingShingle |
Enumerative geometry Intersection theory Noether-Lefschetz locus Cukierman, F. Lopez, A.F. Vainsencher, I. Enumeration of surfaces containing an elliptic quartic curve |
| topic_facet |
Enumerative geometry Intersection theory Noether-Lefschetz locus |
| description |
A very general surface of degree at least four in ℙ3 contains no curves other than intersections with surfaces. We find a formula for the degree of the locus of surfaces in ℙ3 of degree at least five which contain some elliptic quartic curves. We also compute the degree of the locus of quartic surfaces containing an elliptic quartic curve, a case not covered by that formula. © 2014 American Mathematical Society. |
| format |
JOUR |
| author |
Cukierman, F. Lopez, A.F. Vainsencher, I. |
| author_facet |
Cukierman, F. Lopez, A.F. Vainsencher, I. |
| author_sort |
Cukierman, F. |
| title |
Enumeration of surfaces containing an elliptic quartic curve |
| title_short |
Enumeration of surfaces containing an elliptic quartic curve |
| title_full |
Enumeration of surfaces containing an elliptic quartic curve |
| title_fullStr |
Enumeration of surfaces containing an elliptic quartic curve |
| title_full_unstemmed |
Enumeration of surfaces containing an elliptic quartic curve |
| title_sort |
enumeration of surfaces containing an elliptic quartic curve |
| url |
http://hdl.handle.net/20.500.12110/paper_00029939_v142_n10_p3305_Cukierman |
| work_keys_str_mv |
AT cukiermanf enumerationofsurfacescontaininganellipticquarticcurve AT lopezaf enumerationofsurfacescontaininganellipticquarticcurve AT vainsencheri enumerationofsurfacescontaininganellipticquarticcurve |
| _version_ |
1807316966615023616 |