Asymptotic base loci on singular varieties

We prove that the non-nef locus and the restricted base locus of a pseudoeffective divisor coincide on KLT pairs. We also extend to KLT pairs F. Russo's characterization of nef and abundant divisors by means of asymptotic multiplier ideals.Comment: Improved exposition. To appear in "Math. Z.

Nakamaye's theorem on log canonical pairs

We generalize Nakamaye's description, via intersection theory, of the augmented base locus of a big and nef divisor on a normal pair with log-canonical singularities or, more generally, on a normal variety with non-lc locus of dimension at most 1. We also generalize Ein-Lazarsfeld-Mustata-Nakamaye-Popa's description, in terms of valuations, of the subvarieties of the restricted base locus of a big divisor on a normal pair with klt singularities.Comment: v2: We removed, in the introduction, the phrase about Choi's papers, as he uses Nakamaye's theorem in the semiample case. Updated references. v3: added reference to Ambro's "Quasi-log varieties". v4: improved exposition in sections 1, 2 and 4; slightly corrected the statement of Lemma 3.

Augmented base loci and restricted volumes on normal varieties

We extend to normal projective varieties defined over an arbitrary algebraically closed field a result of Ein, Lazarsfeld, Musta\c{t}\u{a}, Nakamaye and Popa characterizing the augmented base locus (aka non-ample locus) of a line bundle on a smooth projective complex variety as the union of subvarieties on which the restricted volume vanishes. We also give a proof of the folklore fact that the complement of the augmented base locus is the largest open subset on which the Kodaira map defined by large and divisible multiples of the line bundle is an isomorphism.Comment: 7 pages. v2: we made a small modification of the statement of Lemma 2.4, a few minor corrections and updated reference

First Documentation of Life Cycle Completion of the Alien Rust Pathogen Melampsoridium hiratsukanum in the Eastern Alps Proves Its Successful Establishment in This Mountain Range

Melampsoridium hiratsukanum is an alien rust fungus which has spread pervasively throughout several European countries following introduction into North Europe at the end of the 20th century. The authenticity of several records of the Melampsoridium species infecting alder (Alnus spp.) in the northern hemisphere is questionable, due to the misidentification and confusion that surround many of the older reports. Given this complicated taxonomic history, and since a M. hiratsukanum-like rust is strongly impacting Alnus incana stands in the Alps, probably affecting the bank protection role of this species along rivers, the unambiguous identification of this pathogen was a pressing epidemiological and ecological issue. In this study, field surveys, light (LM) and scanning electron microscopy (SEM), and molecular characterization were put together in an attempt to solve the conundrum. Field monitoring data, LM and SEM analyses of key taxonomic traits (length of ostiolar cells of uredinium, uredinio-spore shape and size, spore echinulation, number and position of germ pores) and ITS-rDNA sequence-based identification, convergently and unambiguously connected the rust that is causing the current epidemic to the non-native M. hiratsukanum. We documented the completion of the M. hiratsukanum life cycle on its two taxonomically unrelated broadleaf/conifer hosts. This is the first report of M. hiratsukanum from naturally infected Larix decidua in Europe

Structural connectivity‐based topography of the human globus pallidus: Implications for therapeutic targeting in movement disorders

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