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Compactified Picard stacks over the moduli space of curves with marked points
http://hdl.handle.net/2307/426
<Title>Compactified Picard stacks over the moduli space of curves with marked points</Title>
<Authors>Mascarenhas Melo, Ana Margarida</Authors>
<Issue Date>2009-05-28</Issue Date>
<Abstract>For any d Z and g, n 0 such that 2g - 2 + n > 0, denote by Picd, g, n
the stack whose sections over a scheme S consist of flat and proper families
: C S of smooth curves of genus g, with n distinct sections si : S C
and a line bundle L of relative degree d over C. Morphisms between two
such objects are given by cartesian diagrams
C
2
// C
S 1
//
si
II
S s
iU
U
such that si 1 = 2 si, 1 i n, together with an isomorphism
3 : L
2(L ).
Picd, g, n is endowed with a natural forgetful map onto Mg, n and it is, of
course, not complete.
The present thesis consists of the construction of an algebraic stack Pd, g, n
with a map d, g, n onto Mg, n with the following properties.
(1) Pd, g, n and d, g, n fit in the following diagram;
Picd, g, n
// Pd, g, n
d, g, n
Mg, n
// Mg, n
(2) d, g, n is universally closed;
(3) Pd, g, n has a geometrically meaningful modular description.
For n = 0 (and g 2), our compactification consists of a stack theoretical
interpretation of Lucia Caporaso's compactification of the universal Picard
variety over Mg. Then, for n > 0 and 2g-2+n > 1, we proceed by induction
in the number of points following the guidelines of Knudsen's construction
of Mg, n.
1</Abstract>Wed, 27 May 2009 22:00:00 GMThttp://hdl.handle.net/2307/4262009-05-27T22:00:00Z