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Search Results: 1 - 10 of 37675 matches for " Daniel Chan "
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Rational curves and ruled orders on surfaces
Daniel Chan,Kenneth Chan
Mathematics , 2011,
Abstract: We study ruled orders. These arise naturally in the Mori program for orders on projective surfaces and morally speaking are orders on a ruled surface ramified on a bisection and possibly some fibres. We describe fibres of a ruled order and show they are in some sense rational. We also determine the Hilbert scheme of rational curves and hence the corresponding non-commutative Mori contraction. This gives strong evidence that ruled orders are examples of the non-commutative ruled surfaces introduced by Van den Bergh.
McKay correspondence for canonical orders
Daniel Chan
Mathematics , 2007,
Abstract: Canonical orders, introduced in the minimal model program for orders, are simultaneous generalisations of Kleinian singularities and their associated skew group rings. In this paper, we construct minimal resolutions of canonical orders via non-commutative cyclic covers and skew group rings. This allows us to exhibit a derived equivalence between minimal resolutions of canonical orders and the skew group ring form of the canonical order in all but one case. The Fourier-Mukai transform used to construct this equivalence allows us to make explicit, the numerical version of the McKay correspondence for canonical orders which, relates the exceptional curves of the minimal resolution to the indecomposable reflexive modules of the canonical order.
Twisted rings and moduli stacks of "fat" point modules in non-commutative projective geometry
Daniel Chan
Mathematics , 2010,
Abstract: The Hilbert scheme of point modules was introduced by Artin-Tate-Van den Bergh to study non-commutative graded algebras. The key tool is the construction of a map from the algebra to a twisted ring on this Hilbert scheme. In this paper, we study moduli stacks of more general "fat" point modules, and show that there is a similar map to a twisted ring associated to the stack. This is used to provide a sufficient criterion for a non-commutative projective surface to be birationally PI. It is hoped that such a criterion will be useful in understanding Mike Artin's conjecture on the birational classification of non-commutative surfaces.
Hilbert schemes for quantum planes are projective
Daniel Chan
Mathematics , 2008,
Abstract: We show that Hilbert schemes for quantum planes are projective.
Exciting news from Clinical Proteomics
Daniel W Chan
Clinical Proteomics , 2011, DOI: 10.1186/1559-0275-8-3
Abstract: Clinical Proteomics is entering a new and exciting era of open access publishing. The journal has now been transferred to BioMed Central, an online only open access publisher, which is part of Springer Science and Business Media. Becoming open access and online will result in immediate and free access to all articles, and faster review and publication times. High visibility will result from all content being made accessible via web search engines, as well as indexing with PubMed and PubMed Central.As you know, personalized medicine is expected to revolutionize health care delivery in the next decade. I believe that targeted proteomic diagnostics and therapeutics will be the basis of personalized molecular medicine. Recent advances in proteomic and bioinformatic technologies, such as mass spectrometry and protein microarrays, have been used successfully to detect disease-associated biomarkers in complex biological specimens such as tissues, cell lysates, serum, plasma, and other body fluids. Extensive validation will be needed to translate these biomarkers into targeted clinical use.Clinical Proteomics is in the position to take advantage of these opportunities by providing a scholarly forum for novel scientific research in the field of translational proteomics, with special emphasis on the application of proteomic technology to all aspects of clinical investigations including academic, clinical laboratory, pharmaceutical and diagnostic industries.We have assembled a strong editorial team of leading scientists in the field of clinical proteomics including Associate Editors Mark Baker, PhD (Sydney, Australia), Robert J. Cotter, PhD (Baltimore, MD, USA), Dennis Hochstrasser, MD (Geneva, Switzerland), Gil Omenn, MD, Ph.D (Ann Arbor, MI, USA) and Hui Zhang, PhD (Baltimore, MD, USA) as well as Editorial Board Members who are outstanding scientists and clinicians in the field of clinical proteomics. I fully expect that Clinical Proteomics will be a truly international jour
Numerically Calabi-Yau orders on surfaces
Daniel Chan,Rajesh Kulkarni
Mathematics , 2004,
Abstract: This is part of an ongoing program to classify maximal orders on surfaces via their ramification data. Del Pezzo and ruled orders have already been classified. In this paper, we classify numerically Calabi-Yau orders which are the noncommutative analogues of surfaces of Kodaira dimension zero.
Conic bundles and Clifford algebras
Daniel Chan,Colin Ingalls
Mathematics , 2011,
Abstract: We discuss natural connections between three objects: quadratic forms with values in line bundles, conic bundles and quaternion orders. We use the even Clifford algebra, and the Brauer-Severi Variety, and other constructions to give natural bijections between these objects under appropriate hypothesis. We then restrict to a surface base and we express the second Chern class of the order in terms $K^3$ and other invariants of the corresponding conic bundle. We find the conic bundles corresponding to minimal del Pezzo quaterion orders and we discuss problems concerning their moduli.
Moduli of bundles on exotic del Pezzo orders
Daniel Chan,Rajesh Kulkarni
Mathematics , 2008,
Abstract: Maximal orders of rank 4 on the projective plane, ramified on a smooth plane quartic are examples of exotic del Pezzo orders. We compute the possible Chern classes for line bundles on such orders and show the moduli space of line bundles with minimal second Chern class is either a point or a smooth genus two curve.
Non-commutative Mori contractions and $\PP^1$-bundles
Daniel Chan,Adam Nyman
Mathematics , 2009,
Abstract: We give a method for constructing maps from a non-commutative scheme to a commutative projective curve. With the aid of Artin-Zhang's abstract Hilbert schemes, this is used to construct analogues of the extremal contraction of a $K$-negative curve with self-intersection zero on a smooth projective surface. This result will hopefully be useful in studying Artin's conjecture on the birational classification of non-commutative surfaces. As a non-trivial example of the theory developed, we look at non-commutative ruled surfaces and, more generally, at non-commutative $\PP^1$-bundles. We show in particular, that non-commutative $\PP^1$-bundles are smooth, have well-behaved Hilbert schemes and we compute its Serre functor. We then show that non-commutative ruled surfaces give examples of the aforementioned non-commutative Mori contractions.
Moduli stacks of Serre stable representations in tilting theory
Daniel Chan,Boris Lerner
Mathematics , 2015,
Abstract: We introduce a new moduli stack, called the Serre stable moduli stack, which corresponds to studying families of point objects in an abelian category with a Serre functor. This allows us in particular, to re-interpret the classical derived equivalence between most concealed-canonical algebras and weighted projective lines by showing they are induced by the universal sheaf on the Serre stable moduli stack. We explain why the method works by showing that the Serre stable moduli stack is the tautological moduli problem that allows one to recover certain nice stacks such as weighted projective lines from their moduli of sheaves. As a result, this new stack should be of interest in both representation theory and algebraic geometry.
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