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作者：Bamler, Richard H.; Cabezas-Rivas, Esther; Wilking, Burkhard
作者单位：University of California System; University of California Berkeley; Goethe University Frankfurt; University of Munster
摘要：We generalize most of the known Ricci flow invariant non-negative curvature conditions to less restrictive negative bounds that remain sufficiently controlled for a short time. As an illustration of the contents of the paper, we prove that metrics whose curvature operator has eigenvalues greater than -1 can be evolved by the Ricci flow for some uniform time such that the eigenvalues of the curvature operator remain greater than -C. Here the time of existence and the constant C only depend on t...
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作者：Li, Yang
作者单位：Imperial College London
摘要：Motivated by the study of collapsing Calabi-Yau 3-folds with a Lefschetz K3 fibration, we construct a complete Calabi-Yau metric on C3 with maximal volume growth, which in the appropriate scale is expected to model the collapsing metric near the nodal point. This new Calabi-Yau metric has singular tangent cone at infinity C2/Z2xC, and its Riemannian geometry has certain non-standard features near the singularity of the tangent cone, which are more typical of adiabatic limit problems. The proof...
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作者：Zhou, Xin; Zhu, Jonathan J.
作者单位：University of California System; University of California Santa Barbara; Harvard University; Princeton University
摘要：In this paper, we develop a min-max theory for the construction of constant mean curvature (CMC) hypersurfaces of prescribed mean curvature in an arbitrary closed manifold. As a corollary, we prove the existence of a nontrivial, smooth, closed, almost embedded, CMC hypersurface of any given mean curvature c. Moreover, if c is nonzero then our min-max solution always has multiplicity one.
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作者：Nicaise, Johannes; Shinder, Evgeny
作者单位：Imperial College London; KU Leuven; University of Sheffield; HSE University (National Research University Higher School of Economics)
摘要：We prove that stable rationality specializes in regular families whose fibers are integral and have at most ordinary double points as singularities. Our proof is based on motivic specialization techniques and the criterion of Larsen and Lunts for stable rationality in the Grothendieck ring of varieties.
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作者：Salter, Nick
作者单位：Columbia University
摘要：Given an ample line bundle on a toric surface, a question of Donaldson asks which simple closed curves can be vanishing cycles for nodal degenerations of smooth curves in the complete linear system. This paper provides a complete answer. This is accomplished by reformulating the problem in terms of the mapping class group-valued monodromy of the linear system, and giving a precise determination of this monodromy group.
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作者：Garcia, Luis E.; Sankaran, Siddarth
作者单位：University of Toronto; University of Manitoba
摘要：We construct natural Green forms for special cycles in orthogonal and unitary Shimura varieties, in all codimensions, and, for compact Shimura varieties of type O(p,2) and U(p,1), we show that the resulting local archimedean height pairings are related to special values of derivatives of Siegel Eisentein series. A conjecture put forward by Kudla relates these derivatives to arithmetic intersections of special cycles, and our results settle the part of his conjecture involving local archimedean...
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作者：Hop Dang Nguyen; Ngo Viet Trung
作者单位：Vietnam Academy of Science & Technology (VAST); Vietnam Academy of Science & Technology (VAST)
摘要：This paper addresses the problem of comparing minimal free resolutions of symbolic powers of an ideal. Our investigation is focused on the behavior of the function depthR/I(t)=dimR-pdI(t)-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\,\mathrm{depth}\,}}R/I{(t)} = \dim R -{{\,\mathrm{pd}\,}}I{(t)} - 1$$\end{do...
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作者：Cohn, Henry; Goncalves, Felipe
作者单位：Microsoft; University of Alberta; University of Bonn
摘要：We prove an optimal bound in twelve dimensions for the uncertainty principle of Bourgain, Clozel, and Kahane. Suppose f : R-12 -> R is an integrable function that is not identically zero. Normalize its Fourier transform (f) over cap by (f) over cap(xi) = integral(Rd) f(x)e(-2 pi i < x,xi >) dx, and suppose (f) over cap is real-valued and integrable. We show that if f (0) <= 0, (f) over cap (0) <= 0, f (x) = 0 for vertical bar x vertical bar >= r(1), and (f) over cap(xi) = 0 for vertical bar xi...
