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Inhalt des Dokuments

Leitung

Prof. Dr. Peter Bürgisser

Lupe [1]

Anschrift
Technische Universität Berlin
Institut für Mathematik
Sekretariat MA 3-2
Straße des 17. Juni 136
10623 Berlin

Büro
Raum MA 317 (3. OG)
Institut für Mathematik

Kontakt

Sekretariat
Beate Nießen [2]
Raum MA 318
Tel.: +49 (0)30 314 - 25771

eMail
peter.buergisser@offmath.tu-berlin.de
contact form [3]

Telefon
+49 (0)30 314 - 75902
Faxgerät
+49 (0)30 314 - 25839

Sprechstunde
Während der Vorlesungszeit: Mittwochs 1200-1300.
Während der vorlesungsfreien Zeit: Nach Vereinbarung.

Publikationen

Condition of intersecting a projective variety with a varying linear subspace
Zitatschlüssel B-Condition-Of-Intersecting-A-Projective-Variety-With-A-Varying-Linear-Subspace
Autor Peter Bürgisser
Jahr 2015
Monat 10
Notiz To appear in SIAGA.
Zusammenfassung The numerical condition of the problem of intersecting a fixed $m$-dimensional irreducible complex projective variety $Zsubseteqmathbb P^n$ with a varying linear subspace $Lsubseteqmathbb P^n$ of complementary dimension $s=n-m$ is studied. We define the intersection condition number $kappa_Z(L,z)$ at a smooth intersection point $zin Zcap L$ as the norm of the derivative of the locally defined solution map $mathbb G(mathbb P^n,s)tomathbb P^n,, Lmapsto z$. We show that $kappa_Z(L,z) = 1/sinalpha$, where α is the minimum angle between the tangent spaces $T_zZ$ and $T_zL$. From this, we derive a condition number theorem that expresses $1/kappa_Z(L,z)$ as the distance of $L$ to the local Schubert variety, which consists of the linear subspaces having an ill-posed intersection with $Z$ at $z$. A probabilistic analysis of the maximum condition number $kappa_Z(L) := max kappa_Z(L,z_i)$, taken over all intersection points $z_iin Zcap L$, leads to the study of the volume of tubes around the Hurwitz hypersurface $Sigma(Z)$. As a first step towards this, we prove that $vol(Sigma(Z))/vol(mathbb G(mathbb P^n,s)) = pi^-1 (s+1)(n-s) deg(Sigma(Z))$.
Link zur Publikation [4] Download Bibtex Eintrag [5]
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