181 research outputs found
Freshwater actinopterygians of the Los Rastros Formation (Triassic), Bermejo Basin, Argentina
Conformal blocks and generalized theta functions
Let M(r) be the moduli space of rank r vector bundles with trivial
determinant on a Riemann surface X . This space carries a natural line bundle,
the determinant line bundle L . We describe a canonical isomorphism of the
space of global sections of L^k with a space known in conformal field theory as
the ``space of conformal blocks", which is defined in terms of representations
of the Lie algebra sl(r, C((z))).Comment: 43 pages, Plain Te
Filtered screens and augmented Teichm\"uller space
We study a new bordification of the decorated Teichm\"uller space for a
multiply punctured surface F by a space of filtered screens on the surface that
arises from a natural elaboration of earlier work of McShane-Penner. We
identify necessary and sufficient conditions for paths in this space of
filtered screens to yield short curves having vanishing length in the
underlying surface F. As a result, an appropriate quotient of this space of
filtered screens on F yields a decorated augmented Teichm\"uller space which is
shown to admit a CW decomposition that naturally projects to the augmented
Teichm\"uller space by forgetting decorations and whose strata are indexed by a
new object termed partially oriented stratum graphs.Comment: Final version to appear in Geometriae Dedicat
On some differential-geometric aspects of the Torelli map
In this note we survey recent results on the extrinsic geometry of the
Jacobian locus inside . We describe the second fundamental form
of the Torelli map as a multiplication map, recall the relation between totally
geodesic subvarieties and Hodge loci and survey various results related to
totally geodesic subvarieties and the Jacobian locus.Comment: To appear on Boll. UMI, special volume in memory of Paolo de
Bartolomei
Spectral curves and the mass of hyperbolic monopoles
The moduli spaces of hyperbolic monopoles are naturally fibred by the
monopole mass, and this leads to a nontrivial mass dependence of the
holomorphic data (spectral curves, rational maps, holomorphic spheres)
associated to hyperbolic multi-monopoles. In this paper, we obtain an explicit
description of this dependence for general hyperbolic monopoles of magnetic
charge two. In addition, we show how to compute the monopole mass of higher
charge spectral curves with tetrahedral and octahedral symmetries. Spectral
curves of euclidean monopoles are recovered from our results via an
infinite-mass limit.Comment: 43 pages, LaTeX, 3 figure
A local families index formula for d-bar operators on punctured Riemann surfaces
Using heat kernel methods developed by Vaillant, a local index formula is
obtained for families of d-bar operators on the Teichmuller universal curve of
Riemann surfaces of genus g with n punctures. The formula also holds on the
moduli space M{g,n} in the sense of orbifolds where it can be written in terms
of Mumford-Morita-Miller classes. The degree two part of the formula gives the
curvature of the corresponding determinant line bundle equipped with the
Quillen connection, a result originally obtained by Takhtajan and Zograf.Comment: 47 page
Deformation of canonical morphisms and the moduli of surfaces of general type
In this article we study the deformation of finite maps and show how to use
this deformation theory to construct varieties with given invariants in a
projective space. Among other things, we prove a criterion that determines when
a finite map can be deformed to a one--to--one map. We use this criterion to
construct new simple canonical surfaces with different and . Our
general results enable us to describe some new components of the moduli of
surfaces of general type. We also find infinitely many moduli spaces having one component whose general point corresponds to a
canonically embedded surface and another component whose general point
corresponds to a surface whose canonical map is a degree 2 morphism.Comment: 32 pages. Final version with some simplifications and clarifications
in the exposition. To appear in Invent. Math. (the final publication is
available at springerlink.com
Analytic calculations of trial wave functions of the fractional quantum Hall effect on the sphere
We present a framework for the analytic calculations of the hierarchical wave
functions and the composite fermion wave functions in the fractional quantum
Hall effect on the sphere by using projective coordinates. Then we calculate
the overlaps between these two wave functions at various fillings and small
numbers of electrons. We find that the overlaps are all most equal to one. This
gives a further evidence that two theories of the fractional quantum Hall
effect, the hierarchical theory and the composite fermion theory, are
physically equivalent.Comment: 37 pages, revte
Systems of Hess-Appel'rot type
We construct higher-dimensional generalizations of the classical
Hess-Appel'rot rigid body system. We give a Lax pair with a spectral parameter
leading to an algebro-geometric integration of this new class of systems, which
is closely related to the integration of the Lagrange bitop performed by us
recently and uses Mumford relation for theta divisors of double unramified
coverings. Based on the basic properties satisfied by such a class of systems
related to bi-Poisson structure, quasi-homogeneity, and conditions on the
Kowalevski exponents, we suggest an axiomatic approach leading to what we call
the "class of systems of Hess-Appel'rot type".Comment: 40 pages. Comm. Math. Phys. (to appear
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