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Cohomology of the Moduli Space of Cubic Threefolds and Its Smooth Models
We compute and compare the (intersection) cohomology of various natural geometric compactifications of the moduli space of cubic
threefolds: the GIT compactification and its Kirwan blowup, as well as the Baily–Borel and toroidal compactifications of the ball
quotient model, due to Allcock–Carlson–Toledo. Our starting point is Kirwan’s method. We then follow by investigating the behavior of
the cohomology under the birational maps relating the various models, using the decomposition theorem in different ways, and via a
detailed study of the boundary of the ball quotient model. As an easy illustration of our methods, the simpler case of the moduli space
of cubic surfaces is discussed in an appendix.
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Deformation and Unobstructedness of Determinantal Schemes
A closed subscheme
First of all, we compute an upper
The
work contains many examples which illustrate the results obtained and a considerable number of open problems; some of them are collected
as conjectures in the final section.
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Inflectionary Invariants for Isolated Complete Intersection Curve Singularities
We investigate the role played by curve singularity germs in the enumeration of inflection points in families of curves acquiring
singular members. Let
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Explicit Arithmetic of Jacobians of Generalized Legendre Curves Over Global Function Fields
The authors study the Jacobian $J$ of the smooth projective curve $C$ of genus $r-1$ with affine model $y^r = x^r-1(x + 1)(x + t)$ over the function field $\\mathbb F_p(t)$, when $p$ is prime and $r\\ge 2$ is an integer prime to $p$. When $q$ is a power of $p$ and $d$ is a positive integer, the authors compute the $L$-function of $J$ over $\\mathbb F_q(t^1/d)$ and show that the Birch and Swinnerton-Dyer conjecture holds for $J$ over $\\mathbb F_q(t^1/d)$.
eBook
The Irreducible Subgroups of Exceptional Algebraic Groups
This paper is a contribution to the study of the subgroup structure of exceptional algebraic groups over algebraically closed fields
of arbitrary characteristic. Following Serre, a closed subgroup of a semisimple algebraic group
A result of Liebeck and Testerman shows that each irreducible connected subgroup
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