538 research outputs found
Determining plane curve singularities from its polars
This paper addresses a very classical topic that goes back at least to
Pl\"ucker: how to understand a plane curve singularity using its polar curves.
Here, we explicitly construct the singular points of a plane curve singularity
directly from the weighted cluster of base points of its polars. In particular,
we determine the equisingularity class (or topological equivalence class) of a
germ of plane curve from the equisingularity class of generic polars and
combinatorial data about the non-singular points shared by them.Comment: 22 pages. Final version, to appear in Advances in Mat
Constancy regions of mixed multiplier ideals in two-dimensional local rings with rational singularities
The aim of this paper is to study mixed multiplier ideals associated with a tuple of ideals in a two-dimensional local ring with a rational singularity. We are interested in the partition of the real positive orthant given by the regions where the mixed multiplier ideals are constant. In particular we reveal which information encoded in a mixed multiplier ideal determines its corresponding jumping wall and we provide an algorithm to compute all the constancy regions, and their corresponding mixed multiplier ideals, in any desired range.Peer ReviewedPostprint (author's final draft
Spectral analysis of Markarian 421 and Markarian 501 with HAWC
The Hight Altitude Water Cherenkov (HAWC) Gamma-Ray Observatory monitors the
gamma-ray sky in the energy range from 100 GeV to 100 TeV and has detected two
very high energy (VHE) blazars: Markarian 421 (Mrk 421) and Markarian 501 (Mrk
501) in 1.5 years of observations. In this work, we present the spectral
analysis above 1 TeV of both sources using a maximum likelihood method and an
artificial neural network as an energy estimator. The main objectives are to
constrain the spectral curvature of Mrk 421 and Mrk 501 at 5 TeV using
the EBL models from Gilmore et al. (2012) and Franceschini et al. (2008).Comment: Presented at the 35th International Cosmic Ray Conference (ICRC2017),
Bexco, Busan, Korea. See arXiv:1708.02572 for all HAWC contribution
The minimal Tjurina number of irreducible germs of plane curve singularities
In this paper we give a positive answer to a question of Dimca and Greuel
about the quotient between the Milnor and the Tjurina numbers for any
irreducible germ of plane curve singularity. This result is based on a closed
formula for the minimal Tjurina number of an equisingularity class in terms of
the sequence of multiplicities of the strict transform along a resolution. The
key points for the proof are previous results by Genzmer, Wall and Mattei.Comment: To appear in Indiana University Mathematics Journal. Minor changes.
Improvement in Corollary
Multiplicity and Poincaré series for mixed multiplier ideals
Postprint (published version
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