34 research outputs found
Tropical degenerations and stable rationality
No full textWe use the motivic obstruction to stable rationality introduced by Shinder
and the first-named author to establish several new classes of stably
irrational hypersurfaces and complete intersections. In particular, we show
that very general quartic fivefolds and complete intersections of a quadric and a cubic in are stably irrational. An important new ingredient is the use of tropical degeneration techniques
Derived categories and K-groups of singular varieties
No full textThis thesis consists of three parts and is a collection of papers written by the author of this text during his postgraduate studies, together with an Appendix chapter.
The first chapter is based on [98] and is in collaboration with Evgeny Shinder. It discusses the K-groups K_1, K_0 and K_{−n} of the singularity category of isolated quotient singularities. The second chapter is based on [73] and is joint with Martin Kalck and Evgeny Shinder. It introduces Kawamata type semiorthogonal decompositions for singular varieties and obstructions for such decompositions are studied, mainly for the case of nodal threefolds. Each of these two chapters can be read independently. The third chapter is an Appendix to the first chapter and explains in more detail how the main technical result in chapter one is proven, on which the main theorems rely on
Variation of stable birational types of hypersurfaces
No full textWe introduce and study the question how can stable birational types vary in a smooth proper family. Our starting point is the specialization for stable birational types of Nicaise and the author and our emphasis is on stable birational types of hypersurfaces. Building up on the work of Totaro and Schreieder on stable irrationality of hypersurfaces of high degree, we show that smooth Fano hypersurfaces of large degree over a field of characteristic zero are in general not stably birational to each other. In the appendix Claire Voisin proves a similar result in a different setting using the Chow decomposition of diagonal and unramified cohomology
Mitochondria as a sequestration site for incomplete TCRβ peptides: The TCRβ transmembrane domain is a sufficient mitochondrial targeting signal
No full textShear forces promote lymphocyte migration across vascular endothelium bearing apical chemokines
No full textDerived categories of Fano threefolds and degenerations
No full textUsing the technique of categorical absorption of singularities we prove that the nontrivial components of the derived categories of del Pezzo threefolds of degree and crepant categorical resolutions of the nontrivial components of the derived categories of nodal del Pezzo threefolds of degree can be smoothly deformed to the nontrivial components of the derived categories of prime Fano threefolds of genus . This corrects and proves the Fano threefolds conjecture of the first author from [Kuz09], and opens a way to interesting geometric applications, including a relation between the intermediate Jacobians and Hilbert schemes of curves of the above threefolds. We also describe a compactification of the moduli stack of prime Fano threefolds endowed with an appropriate exceptional bundle and its boundary component that corresponds to degenerations associated with del Pezzo threefolds.39 pages; v4: final versio
Derived categories of Fano threefolds and degenerations
No full textUsing the technique of categorical absorption of singularities we prove that the nontrivial components of the derived categories of del Pezzo threefolds of degree d∈{2,3,4,5} and crepant categorical resolutions of the nontrivial components of the derived categories of nodal del Pezzo threefolds of degree d=1 can be smoothly deformed to the nontrivial components of the derived categories of prime Fano threefolds of genus g=2d+2∈{4,6,8,10,12}. This corrects and proves the Fano threefolds conjecture of the first author from (Kuznetsov in Tr. Mat. Inst. Steklova 264:116–128, 2009), and opens a way to interesting geometric applications, including a relation between the intermediate Jacobians and Hilbert schemes of curves of the above threefolds. We also describe a compactification of the moduli stack of prime Fano threefolds endowed with an appropriate exceptional bundle and its boundary component that corresponds to degenerations associated with del Pezzo threefolds
The Drosophila blood brain barrier is maintained by GPCR-dependent dynamic actin structures
No full textThe blood brain barrier (BBB) is essential for insulation of the nervous system from the surrounding environment. In Drosophila melanogaster, the BBB is maintained by septate junctions formed between subperineurial glia (SPG) and requires the Moody/G protein–coupled receptor (GPCR) signaling pathway. In this study, we describe novel specialized actin-rich structures (ARSs) that dynamically form along the lateral borders of the SPG cells. ARS formation and association with nonmuscle myosin is regulated by Moody/GPCR signaling and requires myosin activation. Consistently, an overlap between ARS localization, elevated Ca2+ levels, and myosin light chain phosphorylation is detected. Disruption of the ARS by inhibition of the actin regulator Arp2/3 complex leads to abrogation of the BBB. Our results suggest a mechanism by which the Drosophila BBB is maintained by Moody/GPCR-dependent formation of ARSs, which is supported by myosin activation. The localization of the ARSs close to the septate junctions enables efficient sealing of membrane gaps formed during nerve cord growth.</jats:p
3D nuclear architecture reveals coupled cell cycle dynamics of chromatin and nuclear pores in the malaria parasite Plasmodium falciparum
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