Porteous formula

In mathematics, the Porteous formula, or Thom–Porteous formula, or Giambelli–Thom–Porteous formula, is an expression for the fundamental class of a degeneracy locus (or determinantal variety) of a morphism of vector bundles in terms of Chern classes. Giambelli's formula is roughly the special case when the vector bundles are sums of line bundles over projective space. Thom (1957) pointed out that the fundamental class must be a polynomial in the Chern classes and found this polynomial in a few special cases, and Porteous (1971) found the polynomial in general. Kempf & Laksov (1974) proved a more general version, and Fulton (1992) generalized it further.

Statement

Given a morphism of vector bundles E, F of ranks m and n over a smooth variety, its k-th degeneracy locus (k ≤ min(m,n)) is the variety of points where it has rank at most k. If all components of the degeneracy locus have the expected codimension (m – k)(n – k) then Porteous's formula states that its fundamental class is the determinant of the matrix of size m – k whose (i, j) entry is the Chern class cn–k+j–i(F – E).

References

Read other articles:

Clyde Arc

Clyde ArcKoordinat55°51′26″N 4°16′57″W / 55.85722°N 4.28250°W / 55.85722; -4.28250Moda transportasiKendaraan bermotor, sepeda dan pejalan kakiMelintasiSungai ClydeLokalGlasgow, SkotlandiaNama resmiClyde ArcKarakteristikLebar22 m (72 ft)Bentang terpanjang96 m (315 ft)SejarahBiaya konstruksi£20.3 juta (Anggaran)Dibuka18 September 2006StatistikTolGratisLokasi Clyde Arc adalah sebuah jembatan yang membentang di Sungai Clyde, Glasgow, Skotla...

 

The Playhouse, Cheltenham

The PlayhouseThe PlayhouseLocation within GloucestershireCoordinates51°53′48″N 2°04′27″W / 51.896805°N 2.074265°W / 51.896805; -2.074265TypeTheatreCapacity186Opened1945Websitecheltplayhouse.org.uk/CheltPlayhouse.dll/Home Cheltenham Playhouse is a community theatre in Cheltenham, England, UK. It opened in 1945 as the Civic Playhouse and was run by the Corporation of Cheltenham; it was taken over by volunteers in 1958 who continue to run the operation as a r...

 

Proses penetrasi atmosfer

Proses penetrasi atmosfer adalah proses dari segala gerakan benda baik yang dibuat oleh manusia ataupun yang berasal dari angkasa luar saat mereka masuk ke dalam atmosfer sebuah planet (dalam hal ini bumi) di mana mereka mempenetrasi atmosfer bumi dari ketinggian batas antara lapisan terluar bumi dan angkasa luar. Deskripsi Benda-benda yang sengaja dibuat oleh manusia untuk mengorbit di luar, saat mereka pulang dari angkasa luar dan harus mempenetrasi atmosfer bumi, di mana prosesnya dikontro...

Austin & Ally

Austin & AllyGenreKomediPembuatKevin Kopelow & Heath SeifertPemeran Ross Lynch Laura Marano Raini Rodriguez Calum Worthy Penggubah lagu tema Joleen Belle Mike McGarity Julia Michaels Lagu pembukaCan't Do It Without You[a]Penata musikRick Butler & Fred RapoportNegara asalAmerika SerikatBahasa asliInggrisJmlh. musim4Jmlh. episode87ProduksiProduser eksekutif Kevin Kopelow & Heath Seifert Rick Nyholm Jeny Quine ProduserCraig Wyrick-SolariPengaturan kameraMulti-kamer...

 

Tales of Arcadia

American science fantasy media franchise Tales of ArcadiaCreated by Guillermo del Toro[1] Daniel Kraus Original workTrollhunters (2015 novel)OwnerNetflix / DreamWorks Animation (Universal Pictures)Years2016–2021Print publicationsNovel(s) Trollhunters (2015) Trollhunters: The Adventure Begins (2017) Trollhunters: Welcome to the Darklands (2017) Trollhunters: The Book of Ga-Huel (2018) Trollhunters: Age of the Amulet (2018) Trollhunters: The Way of the Wizard (2018) Trollhunters: Ango...

 

Soto y Amío

Questa voce o sezione sull'argomento centri abitati della Spagna non cita le fonti necessarie o quelle presenti sono insufficienti. Puoi migliorare questa voce aggiungendo citazioni da fonti attendibili secondo le linee guida sull'uso delle fonti. Segui i suggerimenti del progetto di riferimento. Soto y Amíocomune Soto y Amío – Veduta LocalizzazioneStato Spagna Comunità autonoma Castiglia e León Provincia León TerritorioCoordinate42°46′00.12″N 5°52′59.88″W&...

L'Avvenire dei lavoratori

L'Avvenire dei LavoratoriStato Svizzera Linguaitaliano Periodicitàquotidiano Generestampa nazionale Formatonewsletter Fondazione1897 SedeZurigo EditoreL'Avvenire dei Lavoratori Soc. Coop. Diffusione cartacea4800 (2007) DirettoreAndrea Ermano Sito webwww.avvenirelavoratori.eu   Modifica dati su Wikidata · Manuale «Zurigo, da oltre cent'anni, è la capitale dell'emigrazione socialista italiana. Nelle fasi storiche durante le quali nel nostro Paese è venuta a cessare una visib...

 

Lago Okeechobee

Lago OkeechobeeStato Stati Uniti Stato federatoFlorida Coordinate26°55′59.88″N 80°48′00″W / 26.9333°N 80.8°W26.9333; -80.8Coordinate: 26°55′59.88″N 80°48′00″W / 26.9333°N 80.8°W26.9333; -80.8 Altitudine3,74-5,49 m s.l.m. DimensioniSuperficie1 890 km² Lunghezza58 km Larghezza47 km Profondità massima3,7 m Profondità media2,7 m Volume5,2 km³ Sviluppo costiero197 km IdrografiaImmissari pr...

 

The Possum Drop

Opossum lowered to celebrate the new year The Possum Drop is an annual New Year's Eve event in which an opossum is lowered at midnight. The first documented case of a possum drop was in 1990 in Brasstown, North Carolina.[1] The original event has been discontinued, but a version of it is currently held annually in Tallapoosa, Georgia. Brasstown Drop Clay's Corner, home of the Possum Drop, in Brasstown, NC Brasstown's Possum Drop was initially hosted at Clay's Corner, a convenience sto...

Péninsule italienne

Pour les articles homonymes, voir Italie (homonymie). Cet article est une ébauche concernant la géographie et l’Italie. Vous pouvez partager vos connaissances en l’améliorant (comment ?) selon les recommandations des projets correspondants. Péninsule italienne Image satellite de la péninsule italienne. Localisation Pays Italie Malte Saint-Marin Vatican Coordonnées 42° nord, 14° est Mers Ligure, Tyrrhénienne, Ionienne et Adriatique (mer Méditerranée) Géolocalisa...

 

الإسلام في إيران

جزء من سلسلة مقالات حولالإسلام حسب البلد الإسلام في إفريقيا أنغولا بنين بوتسوانا بوركينا فاسو بوروندي الكاميرون الرأس الأخضر أفريقيا الوسطى نشاد الجزائر جزر القمر الكونغو الديمقراطية الكونغو ساحل العاج جيبوتي مصر غينيا الاستوائية إريتريا إثيوبيا الغابون غامبيا غانا غي...

 

Eleftherios Venizelos

Greek politician; Prime Minister 1910–20 and 1928–33 For the Athens airport, see Athens International Airport. Eleftherios VenizelosΕλευθέριος ΒενιζέλοςVenizelos in 1935Prime Minister of GreeceIn office16 January 1933 – 6 March 1933PresidentAlexandros ZaimisPreceded byPanagis TsaldarisSucceeded byAlexandros OthonaiosIn office5 June 1932 – 4 November 1932PresidentAlexandros ZaimisPreceded byAlexandros PapanastasiouSucceeded byPanagis TsaldarisIn off...

Marco Biagi (politician)

Scottish politician Marco BiagiMinister for Local Government and Community EmpowermentIn office21 November 2014 – 18 May 2016First MinisterNicola SturgeonPreceded byDerek MackaySucceeded byKevin StewartMember of the Scottish Parliament for Edinburgh CentralIn office5 May 2011 – 24 March 2016Preceded bySarah BoyackSucceeded byRuth Davidson Personal detailsBorn (1982-07-31) 31 July 1982 (age 41)Alexandria, West Dunbartonshire, ScotlandPolitical partyScottish National ...

 

Adityapur

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: Adityapur – news · newspapers · books · scholar · JSTOR (December 2021) (Learn how and when to remove this message) Suburb / Satellite city in Jamshedpur, Jharkhand, IndiaAdityapurSuburb / Satellite cityAdityapurLocation in Jharkhand, IndiaShow map of Jharkhand...

 

2014 Indianapolis Colts season

62nd season in franchise history 2014 Indianapolis Colts seasonOwnerJim IrsayGeneral managerRyan GrigsonHead coachChuck PaganoHome fieldLucas Oil StadiumResultsRecord11–5Division place1st AFC SouthPlayoff finishWon Wild Card Playoffs(vs. Bengals) 26–10Won Divisional Playoffs(at Broncos) 24–13 Lost AFC Championship(at Patriots) 7–45Pro BowlersS Mike AdamsCB Vontae DavisWR T. Y. HiltonMLB D'Qwell JacksonQB Andrew LuckP Pat McAfeeK Adam VinatieriAP All-ProsP Pat McAfeeK Adam Vinatie...

List of United States Supreme Court cases, volume 239

Supreme Court of the United States38°53′26″N 77°00′16″W / 38.89056°N 77.00444°W / 38.89056; -77.00444EstablishedMarch 4, 1789; 235 years ago (1789-03-04)LocationWashington, D.C.Coordinates38°53′26″N 77°00′16″W / 38.89056°N 77.00444°W / 38.89056; -77.00444Composition methodPresidential nomination with Senate confirmationAuthorized byConstitution of the United States, Art. III, § 1Judge term lengthl...

 

オルニトレステス

オルニトレステス 生息年代: 中生代後期ジュラ紀、154 Ma PreЄ Є O S D C P T J K Pg N ↓ 復元図 地質時代 中生代ジュラ紀後期（約1億5,400万年前） 分類 ドメイン : 真核生物 Eukaryota 界 : 動物界 Animalia 門 : 脊索動物門 Chordata 亜門 : 脊椎動物亜門 Vertebrata 綱 : 爬虫綱 Reptilia 上目 : 恐竜上目 Dinosauria 目 : 竜盤目 Saurischia 亜目 : 獣脚亜目Theropoda 階級なし : ティラノラプトラ Tyr...

 

Cesarea marittima

Questa voce o sezione sull'argomento siti archeologici di Israele non cita le fonti necessarie o quelle presenti sono insufficienti. Puoi migliorare questa voce aggiungendo citazioni da fonti attendibili secondo le linee guida sull'uso delle fonti. Cesarea marittimaTeatro romano di Cesarea marittimaCiviltàCiviltà romana UtilizzoCittà e porto EpocaI secolo a.C. LocalizzazioneStato Israele DistrettoHaifa Altitudine20 m s.l.m. AmministrazioneSito webwww.parks.org.il/en/reserve...

Washington & Jefferson Presidents

Athletic teams representing Washington & Jefferson College Washington & Jefferson PresidentsUniversityWashington & Jefferson CollegeConferencePresidents' Athletic Conference (primary)MPSF (water polo)NCAADivision IIIAthletic directorScott McGuinnessLocationWashington, PennsylvaniaVarsity teams26Football stadiumCameron StadiumBasketball arenaHenry Memorial CenterBaseball stadiumRoss Memorial ParkSoccer stadiumAlexandre StadiumOther venuesBrooks ParkJanet L. Swanson Tennis CourtsHen...

 

لامين ندياي

هذه المقالة يتيمة إذ تصل إليها مقالات أخرى قليلة جدًا. فضلًا، ساعد بإضافة وصلة إليها في مقالات متعلقة بها. (يونيو 2019) لامين ندياي معلومات شخصية الميلاد 19 يونيو 1995 (29 سنة)  فرنسا  مركز اللعب مدافع الجنسية فرنسا  معلومات النادي النادي الحالي GSI Pontivy [الإنجليزية]‏ ال�...