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7
votes
0answers
347 views

Big tangent bundle

Let $X$ be a nonsingular complex algebraic variety whose tangent bundle is $T_X$. I use Lazarsfeld's book for the definition of a big vector bundle. A line bundle $L$ is big if it has Itaka dimension ...
3
votes
0answers
103 views

Lines on Fano complete intersections

Let $X \subset \mathbb{P}^n$ be a non-singular complete intersection of $s$ hypersurfaces of degrees $d_1,\dots,d_s$ over an algebraically closed field $k$ of characteristic zero. Let $d=d_1 + \dots + ...
3
votes
0answers
207 views

Bound for the Picard number of a Fano 3-fold

Let $X$ be a Fano 3-fold with terminal singularities. Is there some bound (possibly explicit) for the Picard rank of $X$ ? If $X$ is smooth, it is well-known that the bound is $10$, obtained by del ...
2
votes
0answers
170 views

Arithmetic of Fano varieties of lines

Let $k$ be a number field and let $X \subset \mathbb{P}^n$ be a non-singular hypersurface of degree $n-1$. Let $F(X)$ denote the Fano variety of lines of $X$. Then it is known that for general $X$ the ...
2
votes
0answers
136 views

Controlling singularities on log mmp

Suppose all my varieties are complex threefolds $X\rightarrow Y$ over some smooth base curve germ $Y$. We can assume the fibres are Del Pezzo surfaces with generic smooth fibre. If I do (relative) ...