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Similar Journals
 Nagoya Mathematical JournalJournal Prestige (SJR): 0.892 Citation Impact (citeScore): 1Number of Followers: 0      Hybrid journal (It can contain Open Access articles) ISSN (Print) 0027-7630 - ISSN (Online) 2152-6842 Published by Cambridge University Press  [388 journals]
• NMJ volume 238 Cover and Front matter
• PubDate: 2020-06-01T00:00:00.000Z
DOI: 10.1017/S0027763020000045
Issue No: Vol. 238 (2020)

• NMJ volume 238 Cover and Back matter
• PubDate: 2020-06-01T00:00:00.000Z
DOI: 10.1017/S0027763020000057
Issue No: Vol. 238 (2020)

• BRILL–NOETHER THEOREMS AND GLOBALLY GENERATED VECTOR BUNDLES ON
HIRZEBRUCH SURFACES
• Authors: IZZET COSKUN; JACK HUIZENGA
Pages: 1 - 36
Abstract: In this paper, we show that the cohomology of a general stable bundle on a Hirzebruch surface is determined by the Euler characteristic provided that the first Chern class satisfies necessary intersection conditions. More generally, we compute the Betti numbers of a general stable bundle. We also show that a general stable bundle on a Hirzebruch surface has a special resolution generalizing the Gaeta resolution on the projective plane. As a consequence of these results, we classify Chern characters such that the general stable bundle is globally generated.
PubDate: 2020-06-01T00:00:00.000Z
DOI: 10.1017/nmj.2018.17
Issue No: Vol. 238 (2020)

• ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$C$ ++++++++++++ ++++++++ ++++-MATRICES+OF+CLUSTER+ALGEBRAS&rft.title=Nagoya+Mathematical+Journal&rft.issn=0027-7630&rft.date=2020&rft.volume=238&rft.spage=37&rft.epage=46&rft.aulast=CAO&rft.aufirst=PEIGEN&rft.au=PEIGEN+CAO&rft.au=MIN+HUANG,+FANG+LI&rft_id=info:doi/10.1017/nmj.2018.18">A CONJECTURE ON $C$ -MATRICES OF CLUSTER ALGEBRAS
• Authors: PEIGEN CAO; MIN HUANG, FANG LI
Pages: 37 - 46
Abstract: For a skew-symmetrizable cluster algebra ${\mathcal{A}}_{t_{0}}$ with principal coefficients at  $t_{0}$ , we prove that each seed $\unicode[STIX]{x1D6F4}_{t}$ of ${\mathcal{A}}_{t_{0}}$ is uniquely determined by its $C$ -matrix, which was proposed by Fomin and Zelevinsky (Compos. Math. 143 (2007), 112–164) as a conjecture. Our proof is based on the fact that the positivity of cluster variables and sign coherence of $c$ -vectors hold for ${\mathcal{A}}_{t_{0}}$ , which was actually verified in Gross et al. (Canonical bases for cluster algebras, J. Amer. Math. Soc. 31(2) (2018), 497–608). Further discussion is provided in the sign-skew-symmetric case so as to obtain a weak version of the conjecture in this general case.
PubDate: 2020-06-01T00:00:00.000Z
DOI: 10.1017/nmj.2018.18
Issue No: Vol. 238 (2020)

• DETECTING KOSZULNESS AND RELATED HOMOLOGICAL PROPERTIES FROM THE ALGEBRA
STRUCTURE OF KOSZUL HOMOLOGY
• Authors: AMANDA CROLL; ROGER DELLACA, ANJAN GUPTA, JUSTIN HOFFMEIER, VIVEK MUKUNDAN, LIANA M. ŞEGA, GABRIEL SOSA, PEDER THOMPSON, DENISE RANGEL TRACY
Pages: 47 - 85
Abstract: Let $k$ be a field and $R$ a standard graded $k$ -algebra. We denote by $\operatorname{H}^{R}$ the homology algebra of the Koszul complex on a minimal set of generators of the irrelevant ideal of $R$ . We discuss the relationship between the multiplicative structure of $\operatorname{H}^{R}$ and the property that $R$ is a Koszul algebra. More generally, we work in the setting of local rings and we show that certain conditions on the multiplicative structure of Koszul homology imply strong homological properties, such as existence of certain Golod homomorphisms, leading to explicit computations of Poincaré series. As an application, we show that the Poincaré series of all finitely generated modules over a stretched Cohen–Macaulay local ring are rational, sharing a common denominator.
PubDate: 2020-06-01T00:00:00.000Z
DOI: 10.1017/nmj.2018.20
Issue No: Vol. 238 (2020)

• A NOTE ON ENTROPY OF AUTO-EQUIVALENCES: LOWER BOUND AND THE CASE OF
ORBIFOLD PROJECTIVE LINES
• Authors: KOHEI KIKUTA; YUUKI SHIRAISHI, ATSUSHI TAKAHASHI
Pages: 86 - 103
Abstract: Entropy of categorical dynamics is defined by Dimitrov–Haiden–Katzarkov–Kontsevich. Motivated by the fundamental theorem of the topological entropy due to Gromov–Yomdin, it is natural to ask an equality between the entropy and the spectral radius of induced morphisms on the numerical Grothendieck group. In this paper, we add two results on this equality: the lower bound in a general setting and the equality for orbifold projective lines.
PubDate: 2020-06-01T00:00:00.000Z
DOI: 10.1017/nmj.2018.21
Issue No: Vol. 238 (2020)

• HIGHER CODIMENSIONAL UEDA THEORY FOR A COMPACT SUBMANIFOLD WITH UNITARY
FLAT NORMAL BUNDLE
• Authors: TAKAYUKI KOIKE
Pages: 104 - 136
Abstract: Let $Y$ be a compact complex manifold embedded in a complex manifold with unitary flat normal bundle. Our interest is in a sort of the linearizability problem of a neighborhood of $Y$ . As a higher codimensional generalization of Ueda’s result, we give a sufficient condition for the existence of a nonsingular holomorphic foliation on a neighborhood of $Y$ which includes $Y$ as a leaf with unitary-linear holonomy. We apply this result to the existence problem of a smooth Hermitian metric with semipositive curvature on a nef line bundle.
PubDate: 2020-06-01T00:00:00.000Z
DOI: 10.1017/nmj.2018.22
Issue No: Vol. 238 (2020)

• ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$p$ ++++++++++++ ++++++++ ++++-ADIC+CLASSICAL+GROUPS&rft.title=Nagoya+Mathematical+Journal&rft.issn=0027-7630&rft.date=2020&rft.volume=238&rft.spage=137&rft.epage=205&rft.aulast=SKODLERACK&rft.aufirst=DANIEL&rft.au=DANIEL+SKODLERACK&rft.au=SHAUN+STEVENS&rft_id=info:doi/10.1017/nmj.2018.23">INTERTWINING SEMISIMPLE CHARACTERS FOR $p$ -ADIC CLASSICAL GROUPS
• Authors: DANIEL SKODLERACK; SHAUN STEVENS
Pages: 137 - 205
Abstract: Let  $G$ be an orthogonal, symplectic or unitary group over a non-archimedean local field of odd residual characteristic. This paper concerns the study of the “wild part” of an irreducible smooth representation of  $G$ , encoded in its “semisimple character”. We prove two fundamental results concerning them, which are crucial steps toward a complete classification of the cuspidal representations of  $G$ . First we introduce a geometric combinatorial condition under which we prove an “intertwining implies conjugacy” theorem for semisimple characters, both in  $G$ and in the ambient general linear group. Second, we prove a Skolem–Noether theorem for the action of  $G$ on its Lie algebra; more precisely, two semisimple elements of the Lie algebra of  $G$ which have the same characteristic polynomial must be conjugate under an element of  $G$ if there are corresponding semisimple strata which are intertwined by an element of  $G$ .
PubDate: 2020-06-01T00:00:00.000Z
DOI: 10.1017/nmj.2018.23
Issue No: Vol. 238 (2020)

• A NOTE ON THE EQUIVALENCE OF THE PARITY OF CLASS NUMBERS AND THE SIGNATURE
RANKS OF UNITS IN CYCLOTOMIC FIELDS
• Authors: DAVID S. DUMMIT
Pages: 206 - 214
Abstract: We collect some statements regarding equivalence of the parities of various class numbers and signature ranks of units in prime power cyclotomic fields. We correct some misstatements in the literature regarding these parities by providing an example of a prime cyclotomic field where the signature rank of the units and the signature rank of the circular units are not equal.
PubDate: 2020-06-01T00:00:00.000Z
DOI: 10.1017/nmj.2018.42
Issue No: Vol. 238 (2020)

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