On the Chern Number of a Filtration

Rossi, Maria Evelina; Valla, Giuseppe

doi:10.4171/rsmup/121-12

Cited by 7 publications

(6 citation statements)

References 19 publications

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“…We will make repeated use of [21, (22.6)] and [19,Section 3]. See also [23] and [24] for a more general version of these results. The following Corollary was previously observed in [19].…”

Section: Preliminariesmentioning

confidence: 99%

The Chern Numbers and Euler Characteristics of Modules

et al. 2014

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The set of the first Hilbert coefficients of parameter ideals relative to a moduleits Chern coefficients-over a local Noetherian ring codes for considerable information about its structure-noteworthy properties such as that of Cohen-Macaulayness, Buchsbaumness, and of having finitely generated local cohomology. The authors have previously studied the ring case. By developing a robust setting to treat these coefficients for unmixed rings and modules, the case of modules is analyzed in a more transparent manner. Another L. Ghezzi et al. series of integers arise from partial Euler characteristics and are shown to carry similar properties of the module. The technology of homological degree theory is also introduced in order to derive bounds for these two sets of numbers.

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“…We will make repeated use of [21, (22.6)] and [19,Section 3]. See also [23] and [24] for a more general version of these results. The following Corollary was previously observed in [19].…”

Section: Preliminariesmentioning

confidence: 99%

The Chern Numbers and Euler Characteristics of Modules

et al. 2014

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“…Progressively, quadratic bounds of this type were developed for arbitrary m-primary ideals in all dimensions by several authors. As a basic source, [RV2] has a systematic development of these formulas along with a comprehensive bibliography. It also treats more general filtrations which were helpful to us.…”

Section: Introductionmentioning

confidence: 99%

“…Among the formulas which more directly influenced the authors here, we single out two developed in the work of J. Elias ([E1,E2]) and M. E. Rossi and G. Valla ([RV1,RV2]).…”

Section: Introductionmentioning

confidence: 99%

Variation of Hilbert coefficients

Ghezzi

Gotō

Hong

et al. 2013

Proc. Amer. Math. Soc.

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Abstract. For a Noetherian local ring (R, m), the first two Hilbert coefficients, e0 and e1, of the I-adic filtration of an m-primary ideal I are known to code for properties of R, of the blowup of Spec(R) along V (I), and even of their normalizations. We give estimations for these coefficients when I is enlarged (in the case of e1 in the same integral closure class) for general Noetherian local rings.

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“…The engineering only research taking into account mainly the energy aspects seems to be not sufficient to ensure the diffusion of ZEB models: in achieving the ZEB target, a major role will be played by architects and designers, who are amongst the main actors of this revolutionary change. More precisely, because the form of our buildings and cities might change radically because of this new energy requirement, the way architects will take up the challenge of designing ZEBs is crucial, as architects are highly responsible of the form of the city and of its symbolic meanings [4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Photovoltaics and zero energy buildings: a new opportunity and challenge for design

Scognamiglio

Røstvik

2012

Progress in Photovoltaics

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Starting from the end of 2020, all new buildings will have to be Nearly Zero Energy Buildings (Nearly ZEBs-ED 2010/31/EU recast). This new 'energy paradigm' might be a revolution for architecture and for Photovoltaics (PV) too, but there are both cultural and technical obstacles to overcome. There is a need to re-think the way buildings are designed (integrating renewables for being ZE). There is a need to re-think the way PV is designed in buildings. PV will be gaining an increasing relevance in the ZEBs design, thanks to its features and potentialities (suitability for any kind of energy demand of the building, easiness of building integration, cost). In a ZEB scenario, PV is very suitable for generating energy, 'on site' and 'at site'; this enlarges the perspective of use of PV from the architectural scale to a wider scale, including the space close to the building or even to the urban and landscape scale. In such a new context, the existing research on the relationships between PV and architecture, focusing mainly on the way the PV components are used in relation to the envelope (Building-integrated PV/Building-added (Attached) PV), is no longer sufficient. The authors envision possible formal results, opportunities and challenges, for the use of PV in ZEBs, as well as new research issues for the future relationships between PV and ZEBs from the architecture and landscape design point of view.

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On the Chern Number of a Filtration

Cited by 7 publications

References 19 publications

The Chern Numbers and Euler Characteristics of Modules

The Chern Numbers and Euler Characteristics of Modules

Variation of Hilbert coefficients

Photovoltaics and zero energy buildings: a new opportunity and challenge for design

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