1,720,987 research outputs found
On the birational geometry of spaces of complete forms II: Skew-forms
No full textModuli spaces of complete skew-forms are compactifications of spaces of skew-symmetric linear maps of maximal rank on a fixed vector space, where the added boundary divisor is simple normal crossing. In this paper we compute their effective, nef and movable cones, the generators of their Cox rings, and for those spaces having Picard rank two we give an explicit presentation of the Cox ring. Furthermore, we give a complete description of both the Mori chamber and stable base locus decompositions of the effective cone of some spaces of complete skew-forms having Picard rank at most four
On the birational geometry of spaces of complete forms I: Collineations and quadrics
No full textModuli 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 three-dimensional projective space
Birational geometry of moduli spaces of configurations of points on the line
No full textIn this paper, we study the geometry of GIT configurations of n ordered points on P1 both from the birational and the biregular viewpoint. In particular, we prove that any extremal ray of the Mori cone of effective curves of the quotient.P1/n== PGL.2/, taken with the symmetric polarization, is generated by a one dimensional boundary stratum of the moduli space. Furthermore, we develop some technical machinery that we use to compute the canonical divisor and the Hilbert polynomial of.P1/n== PGL.2/ in its natural embedding, and its automorphism group
On the unirationality of quadric bundles
Full text linkWe prove that a general -fold quadric bundle
, over a number field, with
and discriminant of odd degree
is unirational, and that the same holds for
quadric bundles over an arbitrary infinite field provided that
has a point, is otherwise general and . As a
consequence we get the unirationality of a general -fold quadric bundle
with discriminant of odd degree
, and of any smooth -fold quadric bundle
, over an algebraically closed field,
with .Comment: 13 page
Quartic and Quintic Hypersurfaces with Dense Rational Points
Get PDFLet
be a quartic hypersurface of dimension
over an infinite field k. We show that if either
contains a linear subspace
of dimension
or has double points along a linear subspace of dimension
, a smooth k-rational point and is otherwise general, then
is unirational over k. This improves previous results by A. Predonzan and J. Harris, B. Mazur and R. Pandharipande for quartics. We also provide a density result for the k-rational points of quartic
-folds with a double plane over a number field, and several unirationality results for quintic hypersurfaces over a
field
Non-secant defectivity via osculating projections
No full textWe introduce a method to produce bounds for the non secant defectivity of an arbitrary irreducible projective variety, once we know how its osculating spaces behave in families and when the linear projections from them are generically finite. Then we analyze the relative dimension of osculating projections of Grassmannians, and as an application of our techniques we prove that asymptotically the Grassmannian G(r, n), parametrizing r -planes in Pn, is not h-defective for h ≤ ( n+1/r+1 )[log2(r )]. This bound improves the previous one h ≤ n-r/3 + 1, due to H. Abo, G. Ottaviani and C. Peterson, for any r ≥ 4
Ample bodies and Terracini loci of projective varieties
No full textWe introduce the notion of ample body of a projective variety and use it to prove emptiness results for Terracini loci and specific identifiability results for toric and homogeneous varieties
Complete symplectic quadrics and Kontsevich spaces of conics in Lagrangian Grassmannians
No full textA wonderful compactification of an orbit under the action of a semi-simple and simply connected group is a smooth projective variety containing the orbit as a dense open subset, and where the added boundary divisor is simple normal crossing. We construct the wonderful compactification of the space of symmetric and symplectic matrices, and investigate its geometry. As an application, we describe the birational geometry of the Kontsevich spaces parametrizing conics in Lagrangian Grassmannians
Bronowski’s conjecture and the identifiability of projective varieties
No full textLet X ⊂ Phn+h-1 be an irreducible and nondegenerate variety of dimension n. Bronowski's conjecture predicts that X is h-identifiable if and only if the general h-1/-tangential projection τX h-1 W X -→ Pn is birational. In this paper we provide counterexamples to this conjecture. Building on the ideas that led to the counterexamples we manage to prove an amended version of the Bronowski's conjecture for a wide class of varieties and to reduce the identifiability problem for projective varieties to their secant defectiveness
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