Details
| Original language | English |
|---|---|
| Pages (from-to) | 849-864 |
| Number of pages | 16 |
| Journal | Advances in mathematics |
| Volume | 213 |
| Issue number | 2 |
| Publication status | Published - 20 Aug 2007 |
| Externally published | Yes |
Abstract
Let Cox (Sr) be the homogeneous coordinate ring of the blow-up Sr of P2 in r general points, i.e., a smooth Del Pezzo surface of degree 9 - r. We prove that for r ∈ {6, 7}, Proj (Cox (Sr)) can be embedded into Gr / Pr, where Gr is an algebraic group with root system given by the primitive Picard lattice of Sr and Pr ⊂ Gr is a certain maximal parabolic subgroup.
Keywords
- Cox ring, Del Pezzo surface, Homogeneous space
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Advances in mathematics, Vol. 213, No. 2, 20.08.2007, p. 849-864.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Universal torsors of Del Pezzo surfaces and homogeneous spaces
AU - Derenthal, Ulrich
PY - 2007/8/20
Y1 - 2007/8/20
N2 - Let Cox (Sr) be the homogeneous coordinate ring of the blow-up Sr of P2 in r general points, i.e., a smooth Del Pezzo surface of degree 9 - r. We prove that for r ∈ {6, 7}, Proj (Cox (Sr)) can be embedded into Gr / Pr, where Gr is an algebraic group with root system given by the primitive Picard lattice of Sr and Pr ⊂ Gr is a certain maximal parabolic subgroup.
AB - Let Cox (Sr) be the homogeneous coordinate ring of the blow-up Sr of P2 in r general points, i.e., a smooth Del Pezzo surface of degree 9 - r. We prove that for r ∈ {6, 7}, Proj (Cox (Sr)) can be embedded into Gr / Pr, where Gr is an algebraic group with root system given by the primitive Picard lattice of Sr and Pr ⊂ Gr is a certain maximal parabolic subgroup.
KW - Cox ring
KW - Del Pezzo surface
KW - Homogeneous space
UR - http://www.scopus.com/inward/record.url?scp=34248387350&partnerID=8YFLogxK
U2 - 10.1016/j.aim.2007.01.012
DO - 10.1016/j.aim.2007.01.012
M3 - Article
AN - SCOPUS:34248387350
VL - 213
SP - 849
EP - 864
JO - Advances in mathematics
JF - Advances in mathematics
SN - 0001-8708
IS - 2
ER -