Paracanonical base locus, Albanese morphism, and semi-orthogonal indecomposability of derived categories

Motivated by an indecomposability criterion of Xun Lin for the bounded derived category of coherent sheaves on a smooth projective variety $X$, we study the paracanonical base locus of $X$, that is the intersection of the base loci of $\omega_X \otimes P_{\alpha}$, for all $\alpha \in \mathrm{Pic}^0 X$. We prove that this is equal to the relative base locus of $\omega_X$ with respect to the Albanese morphism of $X$. As an application, we get that bounded derived categories of Hilbert schemes of points on certain surfaces do not admit non-trivial semi-orthogonal decompositions. We also have a consequence on the indecomposability of bounded derived categories in families. Finally, our viewpoint allows to unify and extend some results recently appearing in the literature.Comment: 15 pages. The main result now holds for any compact K\"ahler manifol

The generic vanishing theorem of Green and Lazarsfeld

La presente tesi riporta in dettaglio la dimostrazione del teorema di annullamento generico di Green e Lazarsfeld ed alcune delle sue conseguenze, in particolare nel caso di varietà di dimensione di Albanese massima. L'ultimo capitolo è dedicato alla dimostrazione di un teorema di Ein e Lazarsfeld sulle varietà che hanno caratteristica di Eulero olomorfa uguale a 0, ottenuto usando la teoria sviluppata da Green e Lazarsfeld

Syzygies of Kummer varieties

We study syzygies of Kummer varieties proving that their behavior is half of the abelian varieties case. Namely, an $m$-th power of an ample line bundle on a Kummer variety satisfies the Green-Lazarsfeld property $(N_p)$, if $m > \frac{p+2}{2}$.Comment: 12 page

Phase-Field Reaction-Pathway Kinetics of Martensitic Transformations in a Model Fe3Ni Alloy

A three-dimensional phase-field approach to martensitic transformations that uses reaction pathways in place of a Landau potential is introduced and applied to a model of Fe3Ni. Pathway branching involves an unbounded set of variants through duplication and rotations by the rotation point groups of the austenite and martensite phases. Path properties, including potential energy and elastic tensors, are calibrated by molecular statics. Acoustic waves are dealt with via a splitting technique between elastic and dissipative behaviors in a large-deformation framework. The sole free parameter of the model is the damping coefficient associated to transformations, tuned by comparisons with molecular dynamics simulations. Good quantitative agreement is then obtained between both methods.Comment: 4 pages, 3 figure

When I Move, You Move: Coordination in Conversation

Researchers have been interested in the dynamics of human conversation for several decades. One major focus of this line of research has been the mechanisms by which humans coordinate in conversation. To study the coordination of conversation within dyads often requires an understanding of statistical methods, which handle time series data. Traditionally, there are no definitive standards for defining one of the important parameters in time series analysis, window size. Therefore, the purpose of the current project was to elucidate the mechanisms through which conversational coordination emerges by utilizing conversational turn-taking as the basis for choosing the appropriate window size in the time series analysis. Data from previously collected videotaped conversational interactions were analyzed for the presence of movement coordination using an image-differencing algorithm in MATLAB. Additionally, speech signals time-locked to the video segments were examined for vocal synchrony in pitch using Praat. The participants from the original study were asked to engage in three tasks designed to elicit sarcasm. Only data from one of these tasks, discussing an ironic scenario, were analyzed for the current project. There were eleven dyads each contributing one conversation and each lasting between 2 and 8 minutes. It was thought that both movement and pitch were possible coordination mechanisms, but that coordination patterns would only be uncovered by using time series windows adjusted for turn-taking rates in each dyad. Results from windowed cross-correlations revealed that participants significantly coordinated movement. Post-hoc tests revealed an effect of window size on mean correlations. Although not significant, results from the analysis of vocal coordination revealed a pattern of results similar to those from the movement coordination study. This could be due to a lack of statistical power. Interestingly, patterns of movement coordination were found strictly as a function of a vocal parameter: turn-taking. These results suggest a novel approach to the study of conversational coordination and a more crucial role for turn-taking in the emergence of coordinative structures

Stability of syzygy bundles on abelian varieties

We prove that the kernel of the evaluation morphism of global sections - namely the syzygy bundle - of a sufficiently ample line bundle on an abelian variety is stable. This settles a conjecture of Ein-Lazarsfeld-Mustopa, in the case of abelian varieties.Comment: Final version. To appear in Bull. Lond. Math. So

Derived invariants arising from the Albanese map

Let $a_X:X\rightarrow \mathrm{Alb}\, X$ be the Albanese map of a smooth complex projective variety. Roughly speaking in this note we prove that for all $i \geq 0$ and $\alpha\in \mathrm{Pic}^0\, X$, the cohomology ranks $h^i(\mathrm{Alb}\, X, \,{a_X}_* \omega_X\otimes P_\alpha)$ are derived invariants. In the case of varieties of maximal Albanese dimension this proves conjectures of Popa and Lombardi-Popa -including the derived invariance of the Hodge numbers $h^{0,j}$ -- and a weaker version of them for arbitrary varieties. Finally we provide an application to derived invariance of certain irregular fibrations.Comment: 16 pages. Final version to appear on Algebraic Geometr