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Theta functions on varieties with effective anti-canonical class
We show that a large class of maximally degenerating families of
We anticipate that wall structures can be
constructed quite generally from maximal degenerations. The construction given here then provides the homogeneous coordinate ring of the
mirror degeneration along with a canonical basis. The appearance of a canonical basis of sections for certain degenerations points
towards a good compactification of moduli of certain polarized varieties via stable pairs, generalizing the picture for K3 surfaces
[Gross, Hacking, Keel, and Siebert,
eBook
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.
eBook
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
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
eBook
How to grow roses : a comprehensive illustrated directory of types and techniques
\"Roses are one of the world's best-loved flowers, and their sweet scent and long-lasting beauty make them indispensable in the garden. With over 200 varieties described and photographed, this book helps you to choose the right plant for your situation, from a free-flowering old rose to a delicate miniature. A Grower's Guide section shows how to maintain your roses, how to select healthy specimens, how to plant them, when to prune and how to propagate new plants. Whether they are grown singly or in conjunction with other plants, as hedges or ground cover, winding through a tree or in a container, there is a place for a rose in every garden\"--Publisher's description.
Book
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.
eBook