9,769 research outputs found
Projective spaces of a C*-algebra
Based on the projective matrix spaces studied by B. Schwarz and A. Zaks, we
study the notion of projective space associated to a C*-algebra A with a fixed
projection p. The resulting space P(p) admits a rich geometrical structure as a
holomorphic manifold and a homogeneous reductive space of the invertible group
of A. Moreover, several metrics (chordal, spherical, pseudo-chordal,
non-Euclidean - in Schwarz-Zaks terminology) are considered, allowing a
comparison among P(p), the Grassmann manifold of A and the space of positive
elements which are unitary with respect to the bilinear form induced by the
reflection e = 2p-1. Among several metrical results, we prove that geodesics
are unique and of minimal length when measured with the spherical and
non-Euclidean metrics.Comment: 26 pages, Late
Differential Equations on Complex Projective Hypersurfaces of Low Dimension
Let and let be a smooth complex projective hypersurface of
. In this paper we find an effective lower bound for the
degree of , such that every holomorphic entire curve in must satisfy an
algebraic differential equation of order , and also similar bounds
for order . Moreover, for every integer , we show that there are
no such algebraic differential equations of order for a smooth
hypersurface in .Comment: Final version, some minor changes according to referee's suggestions,
to appear in Compositio Mathematic
Special geometry on the moduli space for the two-moduli non-Fermat Calabi-Yau
We clarify the recently proposed method to compute a Special K\"ahler metric
on a Calabi-Yau complex structures moduli space that uses the fact that the
moduli space is a subspace of specific Frobenius manifold. We apply this method
to computing the Special K\"ahler metric in a two-moduli non-Fermat model which
has been unknown until now
On 2D N=(4,4) superspace supergravity
We review some recent results obtained in studying superspace formulations of
2D N=(4,4) matter-coupled supergravity. For a superspace geometry described by
the minimal supergravity multiplet, we first describe how to reduce to
components the chiral integral by using ``ectoplasm'' superform techniques as
in arXiv:0907.5264 and then we review the bi-projective superspace formalism
introduced in arXiv:0911.2546. After that, we elaborate on the curved
bi-projective formalism providing a new result: the solution of the covariant
type-I twisted multiplet constraints in terms of a weight-(-1,-1) bi-projective
superfield.Comment: 18 pages, LaTeX, Contribution to the proceedings of the International
Workshop "Supersymmetries and Quantum Symmetries" (SQS'09), Dubna, July
29-August 3 200
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