Paolo Aluffi

Florida State University

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Francesco Pia

Bowling Green State University

Matilde Marcolli

California Institute of Technology

Carel Faber

Utrecht University

M Policarpo

Università degli Studi del Piemonte Orientale “Amedeo Avogadro”

Leonardo C. Mihalcea

Virginia Tech

Andrea Toso

Università degli Studi del Piemonte Orientale “Amedeo Avogadro”

Massimo Olina

Azienda Ospedaliera Ospedale Maggiore

Changjian Su

Tsinghua University

Jörg Schürmann

University of Münster

R Dosdegani

Azienda Ospedaliera Sant'Andrea

Cooperative Institutions

Università degli Studi del Piemonte Orientale “Amedeo Avogadro”

Azienda Ospedaliero Universitaria Maggiore della Carita

Ospedale Maggiore

University of Turin

Fondazione IRCCS Ca' Granda Ospedale Maggiore Policlinico

Azienda Ospedaliera Ospedale Maggiore

Istituti di Ricovero e Cura a Carattere Scientifico

Novamont (Italy)

A. O. Ordine Mauriziano di Torino

Piedmont University

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Percutaneous Sclerotherapy With OK-432 of a Cervicomediastinal Lymphangioma

The Annals of Thoracic Surgery (2015)

Gloria Golinelli Andrea Toso Giovanni Borello Paolo Aluffi Francesco Pia

Lymphangioma

10.1016/j.athoracsur.2014.10.020

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Citations (12)

THE CHERN–SCHWARTZ–MACPHERSON CLASS OF AN EMBEDDABLE SCHEME

Forum of Mathematics Sigma (2019)

Paolo Aluffi

There is an explicit formula expressing the Chern-Schwartz-MacPherson class of a hypersurface in a nonsingular variety (in characteristic $0$) in terms of the Segre class of its jacobian subscheme; this has been known for a number of years. We generalize this formula to arbitrary embeddable schemes: for every subscheme $X$ of a nonsingular variety $V$, we define an associated subscheme $Y$ of a projective bundle over $V$ and provide an explicit formula for the Chern-Schwartz-MacPherson class of $X$ in terms of the Segre class of $Y$. If $X$ is a local complete intersection, a version of the result yields a direct expression for the Milnor class of $X$.

Hypersurface

Characteristic class

Complete intersection

Projective variety

10.1017/fms.2019.25

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Citations (9)

How many hypersurfaces does it take to cut out a Segre class?

Journal of Algebra (2016)

Paolo Aluffi

Hyperplane

Projective variety

Characteristic class

Closure (psychology)

10.1016/j.jalgebra.2016.10.003

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Citations (3)

Inclusion-Exclusion and Segre Classes

Communications in Algebra (2003)

Paolo Aluffi

Abstract We propose a variation of the notion of Segre class, by forcing a naive ‘inclusion-exclusion’ principle to hold. The resulting class is computationally tractable, and is closely related to Chern-Schwartz-MacPherson classes. We deduce several general properties of the new class from this relation, and obtain an expression for the Milnor class of an arbitrary scheme in terms of this class. Dedicated to Steven L. Kleiman on the occasion of his 60th birthday. Key Words: Segre classesChern classesInclusion-exclusion principle2000 Mathematics Subject Classification: Primary 14C17Secondary 14J17, 57R20 Acknowledgments I thank the Max-Planck-Institut für Mathematik in Bonn, Germany, for the hospitality and support. Thanks are also due to the referee, who spotted several inaccuracies in a preliminary version of this paper. Notes Dedicated to Steven L. Kleiman on the occasion of his 60th birthday. a SMis supposed both to evoke the connection with Schwartz-MacPherson classes, which is the key to the main properties of the class, and the fact that we view this notion as a ‘smoothing’ of the notion of conventional Segre class.

Forcing (mathematics)

10.1081/agb-120022435

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Citations (15)

Pfaffian integrals and invariants of singular varieties

Contemporary mathematics - American Mathematical Society (2020)

Paolo Aluffi Mark Goresky

Integrals of the Pfaffian form over the nonsingular part of a projective variety compute information closely related to the Mather-Chern class of the variety and to other invariants such as the local Euler obstruction along strata of its singular locus and, in the hypersurface case, Milnor numbers. We obtain simple proofs of these formulas, recovering along the way several classically known results.

Pfaffian

Hypersurface

10.1090/conm/742/14935

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Citations (2)

Two characteristic numbers for smooth plane curves of any degree

Transactions of the American Mathematical Society (1992)

Paolo Aluffi

We use a sequence of blow-ups over the projective space parametrizing plane curves of degree $d$ to obtain some enumerative results concerning smooth plane curves of arbitrary degree. For $d = 4$, this gives a first modern verification of results of H. G. Zeuthen.

Degree (music)

10.1090/s0002-9947-1992-1041042-5

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Citations (16)

Chern Classes of Splayed Intersections

Canadian Journal of Mathematics (2015)

Paolo Aluffi Eleonore Faber

We generalize the Chern class relation for the transversal intersection of two nonsingular varieties to a relation for possibly singular varieties, under a 'splayedness' assumption. The relation is shown to hold for both the Chern-Schwartz-MacPherson class and the Chern-Fulton class. The main tool is a formula for Segre classes of splayed subschemes. We also discuss the Chern class relation under the assumption that one of the varieties is a general very ample divisor.

10.4153/cjm-2015-010-7

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Citations (7)

Homological algebra

Graduate studies in mathematics (2009)

Paolo Aluffi

Homological algebra

10.1090/gsm/104/09

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Citations (0)

Isolated Hypoglossal Nerve Palsy Mimicking a Base of Tongue Tumor

Journal of Craniofacial Surgery (2016)

Daniela Francesca Nestola Mariangela Lombardi Matteo Brucoli Francesco Pia Paolo Aluffi

Isolated paralysis of hypoglossal nerve is uncommon, generally being associated with other neuropathies. A careful differential diagnosis is necessary to recognize the underlying diseases, some of which can be life-threatening. The authors report a patient of an 80-year-old woman presenting with an isolated hypoglossal palsy, mimicking a tongue neoplasm. Through a careful clinical workup and thanks to the aid of the imaging, it was possible to identify the presence of signal alterations due to a subacute denervation of the affected hemitongue and to exclude the presence of a tumor. The patient was clinically diagnosed as isolated hypoglossal palsy, resulting from a thrombo-embolic accident involving the nerve along its course. The authors propose some useful means for the differential diagnosis and review the literature.

Hypoglossal nerve

Cranial nerve palsy

10.1097/scs.0000000000003240

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Citations (7)

Grothendieck Classes and Chern Classes of Hyperplane Arrangements

International Mathematics Research Notices (2012)

Paolo Aluffi

Journal Article Grothendieck Classes and Chern Classes of Hyperplane Arrangements Get access Paolo Aluffi Paolo Aluffi Department of Mathematics, Florida State University, Tallahassee, FL 32306, USA Correspondence to be sent to: aluffi@math.fsu.edu Search for other works by this author on: Oxford Academic Google Scholar International Mathematics Research Notices, Volume 2013, Issue 8, 2013, Pages 1873–1900, https://doi.org/10.1093/imrn/rns100 Published: 24 March 2012 Article history Received: 07 October 2011 Revision received: 06 January 2012 Accepted: 22 February 2012 Published: 24 March 2012

Hyperplane

10.1093/imrn/rns100

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Citations (40)