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Mathematics > Algebraic Geometry

arXiv:1803.09161 (math)
[Submitted on 24 Mar 2018 (v1), last revised 31 Mar 2018 (this version, v2)]

Title:On the birational geometry of spaces of complete forms I: collineations and quadrics

Authors:Alex Massarenti
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Abstract:Moduli spaces of complete collineations are wonderful compactifications of spaces of linear maps of maximal rank between two fixed vector spaces. We investigate the birational geometry of moduli spaces of complete collineations and quadrics from the point of view of Mori theory. We compute their effective, nef and movable cones, the generators of their Cox rings, and their groups of pseudo-automorphisms. Furthermore, we give a complete description of both the Mori chamber and stable base locus decompositions of the effective cone of the space of complete collineations of the 3-dimensional projective space.
Comments: 38 pages
Subjects: Algebraic Geometry (math.AG); Representation Theory (math.RT)
MSC classes: 14E30 (Primary), 14J45, 14N05, 14E07, 14M27 (Secondary)
Cite as: arXiv:1803.09161 [math.AG]
  (or arXiv:1803.09161v2 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1803.09161
Related DOI: https://doi.org/10.1112/plms.12377

Submission history

From: Alex Massarenti [view email]
[v1] Sat, 24 Mar 2018 20:47:47 UTC (43 KB)
[v2] Sat, 31 Mar 2018 14:15:05 UTC (44 KB)
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