A quantitative version of the converse Taylor theorem: $C^{k,ω}$-smoothness

Michal Johanis

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Relations between moduli of smoothness of the derivatives of a function and those of the function itself are investigated. The results are for $L_{p} (T)$ and $L_{p} [- 1, 1]$ for 0 < p < ∞ using the moduli of smoothness $ω^{r} {(f, t)}_{p}$ and $ω_{φ}^{r} {(f, t)}_{p}$ respectively.

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Gavril Farkas, Katharina Ludwig (2010)

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We study the enumerative geometry of the moduli space $ℛ_{g}$ of Prym varieties of dimension $g - 1$ . Our main result is that the compactication of $ℛ_{g}$ is of general type as soon as $g > 13$ and $g$ is different from 15. We achieve this by computing the class of two types of cycles on $ℛ_{g}$ : one defined in terms of Koszul cohomology of Prym curves, the other defined in terms of Raynaud theta divisors associated to certain vector bundles on curves. We formulate a Prym–Green conjecture on syzygies of Prym-canonical...

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Inspired by the ideas of the minimal model program, Shepherd-Barron, Kollár, and Alexeev have constructed a geometric compactification for the moduli space of surfaces of log general type. In this paper, we discuss one of the simplest examples that fits into this framework: the case of pairs $(X, H)$ consisting of a degree two $K 3$ surface $X$ and an ample divisor $H$ . Specifically, we construct and describe explicitly a geometric compactification ${\bar{P}}_{2}$ for the moduli of degree two $K 3$ pairs. This compactification...

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In this paper we consider questions of the following type. Let $k$ be a base field and $K / k$ be a field extension. Given a geometric object $X$ over a field $K$ (e.g. a smooth curve of genus $g$ ), what is the least transcendence degree of a field of definition of $X$ over the base field $k$ ? In other words, how many independent parameters are needed to define $X$ ? To study these questions we introduce a notion of essential dimension for an algebraic stack. Using the resulting theory, we give a complete...

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Displaying similar documents to “A quantitative version of the converse Taylor theorem: C k , ω -smoothness”

Displaying similar documents to “A quantitative version of the converse Taylor theorem: $C^{k, ω}$ -smoothness”