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作者：Mikhalkin, Grigory; Orevkov, Stepan
作者单位：University of Geneva; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：Oleg Viro introduced an invariant of rigid isotopy for real algebraic knots and links in RP3 which is not a topological isotopy invariant. In this paper we study real algebraic links of degree d with the maximal value of this invariant. We show that these links admit entirely topological description. In particular, these links are characterized by the property that any of their planar diagram has at least (d-1)(d-2)/2-g-1 crossing points where g is the genus of the complexification. Also we sh...
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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：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.
