13,375 research outputs found
Computing Puiseux series : a fast divide and conquer algorithm
Let be a polynomial of total degree defined over
a perfect field of characteristic zero or greater than .
Assuming separable with respect to , we provide an algorithm that
computes the singular parts of all Puiseux series of above in less
than operations in , where
is the valuation of the resultant of and its partial derivative with
respect to . To this aim, we use a divide and conquer strategy and replace
univariate factorization by dynamic evaluation. As a first main corollary, we
compute the irreducible factors of in up to an
arbitrary precision with arithmetic
operations. As a second main corollary, we compute the genus of the plane curve
defined by with arithmetic operations and, if
, with bit operations
using a probabilistic algorithm, where is the logarithmic heigth of .Comment: 27 pages, 2 figure
Stability Conditions and Lagrangian Cobordisms
In this paper we study the interplay between Lagrangian cobordisms and
stability conditions. We show that any stability condition on the derived
Fukaya category of a symplectic manifold
induces a stability condition on the derived Fukaya category of Lagrangian
cobordisms . In addition, using stability
conditions, we provide general conditions under which the homomorphism , introduced by Biran and Cornea, is
an isomorphism. This yields a better understanding of how stability conditions
affect and it allows us to elucidate Haug's result, that the
Lagrangian cobordism group of is isomorphic to
.Comment: 53 pages, 3 figures, expansions and revisions, improvement of
expositio
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