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UID:8703@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20250620T140000
DTEND;TZID=Europe/Paris:20250620T150000
DTSTAMP:20250615T161704Z
URL:https://www.i2m.univ-amu.fr/evenements/soutenance-de-these-naoufal-bou
 chareb/
SUMMARY:Naoufal BOUCHAREB (I2M): Soutenance de thèse Naoufal BOUCHAREB
DESCRIPTION:Naoufal BOUCHAREB: We study the classification of affine holomo
 rphic bundles over a compact complex manifold $X$.\n\nThe thesis has two g
 oals: first we prove classification theorems for affine bundles over Riema
 nn surfaces\, notably for affine bundles over the projective line. In part
 icular we study the moduli space of framed\, non-degenerate rank 2 affine 
 bundles over $\\mathbb{P}^1_\\mathbb{C}$ whose linearisation\, viewed as l
 ocally free sheaf\, is isomorphic to $\\mathcal{O}(n_1)\\oplus \\mathcal{O
 }(n_2)$ where $n_1&gt\;n_2$. We show that this moduli space can be identif
 ied with the "topological cokernel" of a morphism of linear spaces over th
 e projective space $\\mathbb{P}(\\mathbb{C}[X_0\,X_1]_{l})$ of binary form
 s of degree $l:= -2-n_2$\, in particular it fibres over this projective sp
 ace with vector spaces as fibres. We show that the stratification of $\\ma
 thbb{P}(\\mathbb{C}[X_0\,X_1]_{l})$ defined by the level sets of the fibre
  dimension map is determined explicitly by $d:= n_1-n_2$ and the cactus ra
 nk stratification of $\\mathbb{P}((\\mathbb{C}[X_0\,X_1]_{l})$.\n\nThe sec
 ond goal has a broader scope: the classification of affine bundles with fi
 xed linearisation type over a compact complex manifold $X$. More precisely
 \, let $E$ be a fixed holomorphic vector bundle over $X$ and $\\mathcal{E}
 $ the associated locally free sheaf. We will assume that there exists an e
 ffective divisor $D$ on $X$ such that $H^1(X\,\\mathcal{E}(D))=0$. This co
 ndition is always satisfied if $X$ is a projective complex manifold.\n\nWe
  define in a natural way the moduli stack of affine bundles on $X$ whose l
 inearisation is isomorphic to $E$\, and we prove that this moduli stack is
  isomorphic to the quotient stack $[H^0(X\,\\mathcal{E}(D)_D)/H^0(X\,\\mat
 hcal{E}(D))\\ltimes \\mathrm{Aut}(E)]$ of the complex vector space $H^0(X\
 ,\\mathcal{E}(D)_D)$ by the semi-direct product of the automorphism group 
 $\\mathrm{Aut}(E)$ (which is always an affine algebraic group) by the comp
 lex vector space $H^0(X\,\\mathcal{E}(D))$.
CATEGORIES:Soutenance de thèse,AGT
LOCATION:I2M Saint-Charles - Salle de séminaire\, Université Aix-Marseill
 e\, Campus Saint-Charles\, 3 Place Victor Hugo\, Marseille\, 13003\, Franc
 e
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=Université Aix-Marseille\,
  Campus Saint-Charles\, 3 Place Victor Hugo\, Marseille\, 13003\, France;X
 -APPLE-RADIUS=100;X-TITLE=I2M Saint-Charles - Salle de séminaire:geo:0,0
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DTSTART:20250330T030000
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