arXiv subjects

Lars Petersen

Publications and source records attributed to Lars Petersen.

7 recordsLinked to original sources

arXiv2015

Merging divisorial with colored fans

Given a spherical homogeneous space G/H of minimal rank, we provide a simple procedure to describe its embeddings as varieties with torus action in terms of divisorial fans. The torus in question is obtained as the identity component of the quotient group N/H, where N is the normalizer of H in G. The resulting Chow quotient is equal to (a blowup of) the simple toroidal compactification of G/(H N^0). In the horospherical case, for example, it is equal to a flag variety, and the slices (coefficients) of the divisorial fan are merely shifts of the colored fan along the colors.

math.AG↗

arXiv2011

Okounkov Bodies of Complexity-One T-Varieties

We compute Okounkov bodies of projective complexity-one T-varieties with respect to two types of invariant flags. In particular, we show that the latter are rational polytopes. Moreover, using results of Dave Anderson and Nathan Ilten, we briefly exhibit explicit links to degenerations and T-deformations. Finally, we prove that the global Okounkov body of a rational projective complexity-one T-variety is rational polyhedral.

math.AG↗

arXiv2011

The Geometry of T-Varieties

This is a survey of the language of polyhedral divisors describing T-varieties. This language is explained in parallel to the well established theory of toric varieties. In addition to basic constructions, subjects touched on include singularities, separatedness and properness, divisors and intersection theory, cohomology, Cox rings, polarizations, and equivariant deformations, among others.

math.AG↗

arXiv2010

Torus invariant divisors

Using the language of polyhedral divisors and divisorial fans we describe invariant divisors on normal varieties X which admit an effective codimension one torus action. In this picture X is given by a divisorial fan on a smooth projective curve Y. Cartier divisors on X can be described by piecewise affine functions h on the divisorial fan S whereas Weil divisors correspond to certain zero and one dimensional faces of it. Furthermore we provide descriptions of the divisor class group and the canonical divisor. Global sections of line bundles O(D_h) will be determined by a subset of a weight polytope associated to h, and global sections of specific line bundles on the underlying curve Y.

math.AG↗

arXiv2010

Cox rings of rational complexity one T-varieties

Let X be a Mori dream space together with an effective torus action of complexity one. In this note, we construct a polyhedral divisor on a suitable covering of the projective line P^1 which corresponds to the affine spectrum of the Cox ring of X. This description allows for a detailed study of torus orbits and deformations of the latter. Moreover, we present coverings of P^1 together with an action of a finite abelian group A in terms of so-called A-divisors of degree zero on P^1.

math.AG↗

arXiv1997

Dust extinction of HII regions in NGC 598 and NGC 5457

The dust extinction towards bright HII regions in NGC 598 and NGC 5457 has been studied in detail by forming line ratios of Balmer and Paschen emission lines covering a large wavelength range. Three homogeneous models of the geometrical distribution of the emitting sources and the obscuring dust have been tested. Only for low extinctions can the data be fit by a homogeneous slab. For most of the observed HII regions the Witt et al.(1992) 'dusty nucleus' model matches the observations equally well as the usual assumption of a foreground screen, but the former implies much larger actual dust contents. Spatial variations in the optical depth in V of the order 0.3 across a region are found.

astro-ph↗

arXiv1996

A sulphur abundance study of NGC 300 by an empirical calibration method

We propose an empirical sulphur abundance determination method based on the strong sulphur emission lines, [S II] 6716, 6731 and [S III] 9069, 9531 in H II regions. From a compilation of literature data we have made a calibration of sulphur abundance versus ([S II] + [S III])/Hbeta, similar to what has been widely used for the more easily observable iso-electronic element oxygen. This enables abundance determinations in extragalactic H II regions without measurements of weak temperature sensitive lines for use in model calculations. As a first application of the empirical calibration 15 spectra covering the wavelength range 3650-10000 AA have been obtained of H II regions at various galactocentric distances in the spiral galaxy NGC 300, by employing specially designed multiaperture slitmasks which allow simultaneous observations of several H II regions. Sulphur and oxygen abundances are determined and an oxygen gradient in agreement with previously published work is found as well as a somewhat steeper sulphur abundance gradient. This results in a slight decrease of log S/O with increasing radius. The quite low values of S/O seem to confirm the trend demonstrated by Diaz et al. (1991) of a decrease in log S/O at high metallicities, but still more data are needed before any definite conclusions can be drawn. We find as expected that the radiation softness parameter eta decreases with increasing radius and the slope is comparable to what is found for spiral galaxies of similar metallicity.

astro-ph↗