Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics: Festschrift for Antonio Campillo on the Occasion of his 65th Birthday

604 Pages·2018·11.76 MB·English

by  Gert-Martin Greuel

Gert-Martin Greuel 
Luis Narváez Macarro
Sebastià Xambó-Descamps E ditors
Singularities,
Algebraic Geometry,
Commutative Algebra,
and Related Topics
Festschrift for Antonio Campillo on the
Occasion of his 65th Birthday
Singularities, Algebraic Geometry,
Commutative Algebra, and Related Topics
Gert-Martin Greuel • Luis Narváez Macarro (cid:129)
`
Sebastia Xambó-Descamps
Editors
Singularities,
Algebraic Geometry,
Commutative Algebra,
and Related Topics
Festschrift for Antonio Campillo
on the Occasion of his 65th Birthday
123
Editors
Gert-MartinGreuel LuisNarváezMacarro
FachbereichMathematik DepartamentodeÁlgebra
Universita¨tKaiserslautern InstitutodeMatemáticas(IMUS)
Kaiserslautern,Germany UniversidaddeSevilla
Sevilla,Spain
Sebastia`Xambó-Descamps
DepartamentdeMatema`tiques
UniversitatPolite`cnicadeCatalunya
Barcelona,Spain
ISBN978-3-319-96826-1 ISBN978-3-319-96827-8 (eBook)
https://doi.org/10.1007/978-3-319-96827-8
LibraryofCongressControlNumber:2018955477
MathematicsSubjectClassification(2010):14-XX,32SXX,11AXX,13PXX,19DXX,37FXX,51EXX,
94BXX
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Preface
The decision to prepare a volume of contributions in honor of Antonio Campillo
was taken at the University of Valladolid (Spain) during 19–23 June 2017 on
the occasion of the 4th Joint Congress of the Spanish and Mexican Mathematical
Societies.
The Congress paid homage to Campillo by including two plenary lectures to
presenthiscontributionstomathematicsandhisserviceandleadershipinavariety
ofinstitutions,twospecialsessionsonSingularitiesandAlgebraicGeometry,anda
specialscientificdaytocelebratemorecloselyhismathematicalwork.
Theannouncementofthisbookprojectwassenttothelistofallparticipantsat
theCongressenlargedwiththenamesofothercolleagueswithwhomCampillohas
hadsignificantinteractionsinhisprofessionalcareer.
This volume collects the refereed papers that were submitted following that
announcement.After the openingarticle, which is meant to be a first approachto
Campillo’sbiography,we havegroupedthepapersinfivecategories:Singularities
(ten papers), Algebraic Geometry (five), Commutative Algebra (five), Algebraic
Codes(three),and OtherTopics(three).The varietyof topicscorrelateswellwith
theverybroadresearchinterestsofAntonioCampillo.
Thegroupingisofcourseimperfect,assomepaperswouldeasilyfitinmorethan
onecategory,butwehopethattheclassificationrespectsneverthelessthemainarea
inwhicheachpaperisascribed.Withineachcategory,papersthatexplicitlyconnect
with publishedworkof Campillo are placedfirst, andthese, as well as the others,
areorderedalphabeticallybythefamilynameofthefirstauthor.
We are most grateful to all the authors (two per paper on average) for their
positive response, their patience with the long refereeing process, and above all,
for their scientific contribution to the volume. Thanks also to the generosity and
keenjudgmentsofthemanyanonymousreferees.
Going back to the beginning, we are thankful to the Mexican and Spanish
mathematicalsocieties for having embraced the idea of paying tribute to Antonio
Campillo on the occasion of their 4th joint meeting, and to the University of
Valladolid, in particular to its Mathematical Institute (IMUVA), for providing
excellentorganizationforallactivitiesinthatweek.
v
vi Preface
AntonioCampillohasbeenourcolleagueandfriendformanyyears,inavariety
of circumstances, and it is a pleasantduty to expressour acknowledgmentto him
for his productive career, his dedication to causes that promote the welfare of
institutionsand professionalcommunities,his vision regardingacademicprogress
and research organization, his engagement in increasing public awareness of
mathematics,andofcourseforallhisachievementsinmathematics.
We wish you, Antonio, a most happy 65th birthday and that your career may
continue to be, for many years to come, as productive and inspirational as it has
beenhitherto.
Kaiserslautern,Germany Gert-MartinGreuel
Sevilla,Spain LuisNarváezMacarro
Barcelona,Spain SebastiàXambó-Descamps
Contents
AntonioCampillo ................................................................ 1
FranciscoMonserratandSebastiàXambó-Descamps
Singularities in Positive Characteristic: Equisingularity,
Classification,Determinacy..................................................... 37
Gert-MartinGreuel
UltrametricSpacesofBranchesonArborescentSingularities.............. 55
Evelia R. García Barroso, Pedro D. González Pérez,
andPatrickPopescu-Pampu
TwoPointsoftheBoundaryofToricGeometry.............................. 107
BernardTeissier
OntheMilnorFormulainArbitraryCharacteristic ........................ 119
EveliaR.GarcíaBarrosoandArkadiuszPłoski
Foliations in the Plane Uniquely Determined by Minimal
SubschemesofitsSingularities................................................. 135
JorgeOlivares
NewtonTransformationsandtheMotivicMilnorFiberofaPlane
Curve .............................................................................. 145
PierretteCassou-NoguèsandMichelRaibaut
NashModificationonToricCurves............................................ 191
DanielDuarteandDanielGreenTripp
ARecursiveFormulafortheMotivicMilnorFiberofaPlaneCurve ..... 203
ManuelGonzálezVilla,GaryKennedy,andLeeJ.McEwan
OnHasse–SchmidtDerivations:TheActionofSubstitutionMaps ........ 219
LuisNarváezMacarro
AnIntroductiontoResolutionofSingularitiesviatheMultiplicity........ 263
DiegoSulcaandOrlandoVillamayorU.
vii
viii Contents
PlatonicSurfaces................................................................. 319
Brenda Leticia De La Rosa-Navarro, Gioia Failla, Juan Bosco
Frías-Medina,MustaphaLahyane,andRosannaUtano
CoveringsofRationalRuledNormalSurfaces ............................... 343
Enrique Artal Bartolo, José Ignacio Cogolludo-Agustín,
andJorgeMartín-Morales
UlrichBundlesonVeroneseSurfaces.......................................... 375
LauraCostaandRosaMariaMiró-Roig
MultipleStructuresonSmoothonSingularVarieties ....................... 383
M.R.Gonzalez-Dorrego
Smoothness in Some Varieties with Dihedral Symmetry
andtheDFTMatrix ............................................................. 391
SantiagoLópezdeMedrano
TheGreedyAlgorithmandtheCohen-MacaulayPropertyofRings,
GraphsandToricProjectiveCurves........................................... 411
ArgimiroArratia
BinomialIdealsandCongruencesonNn ...................................... 429
LauraFeliciaMatusevichandIgnacioOjeda
The K-TheoryofToricSchemesOverRegularRingsofMixed
Characteristic..................................................................... 455
G.Cortiñas,C.Haesemeyer,M.E.Walker,andC.A.Weibel
OnFiniteandNonfiniteGenerationofAssociatedGradedRingsof
AbhyankarValuations........................................................... 481
StevenDaleCutkosky
Symbolic Powers of Monomial Ideals and Cohen-Macaulay
Vertex-WeightedDigraphs...................................................... 491
PhilippeGimenez,JoséMartínez-Bernal,AronSimis,RafaelH.Villarreal,
andCarlosE.Vivares
AsymptoticsofReducedAlgebraicCurvesOverFiniteFields.............. 511
J.I.Farrán
ThePoincaréPolynomialofaLinearCode ................................... 525
Carlos Galindo, Fernando Hernando, Francisco Monserrat,
andRuudPellikaan
TheMetricStructureofLinearCodes......................................... 537
DiegoRuano
OnSomePropertiesofAInheritedbyCb(X,A)............................. 563
AlejandraGarcía,LourdesPalacios,andCarlosSignoret
Contents ix
AFractionalPartialDifferentialEquationforThetaFunctions............ 579
RafaelG.Campos
OnContinuedFractions......................................................... 593
GerardoGonzalezSprinberg
Contributors
Argimiro Arratia Department of Computer Science and Barcelona Graduate
SchoolofMathematics,UniversitatPolitècnicadeCatalunya,Barcelona,Spain
Enrique Artal Bartolo Departamento de Matemáticas, IUMA, Universidad de
Zaragoza,Zaragoza,Spain
RafaelG.Campos DivisióndeCienciaseIngeniería,DepartamentodeCiencias,
UniversidaddeQuintanaRoo,Chetumal,México
PierretteCassou-Noguès Institut de Mathématiquesde Bordeaux,(UMR 5251),
UniversitédeBordeaux,TalenceCedex,France
JoséIgnacioCogolludo-Agustín DepartamentodeMatemáticas,IUMA,Univer-
sidaddeZaragoza,Zaragoza,Spain
G. Cortiñas Department of Matemática-Inst. Santaló, FCEyN, Universidad de
BuenosAires,BuenosAires,Argentina
Laura Costa Departament de Matemàtiques i Informàtica, Facultat de Matemà-
tiquesiInformàtica,Barcelona,Spain
Steven Dale Cutkosky Department of Mathematics, University of Missouri,
Columbia,MO,USA
Daniel Duarte CONACYT, Universidad Autónoma de Zacatecas, Zacatecas,
Mexico
GioiaFailla UniversitàMediterraneadiReggioCalabria,DIIES,ReggioCalabria,
Italy
J.I.Farrán UniversidaddeValladolid,Valladolid,Spain
xi