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pro vyhledávání: '"Abramovich, Dan"'
We give a formula for the integral Chow rings of weighted blow-ups. Along the way, we also compute the integral Chow rings of weighted projective stack bundles, a formula for the Gysin homomorphism of a weighted blow-up, and a generalization of the s
Externí odkaz:
http://arxiv.org/abs/2307.01459
Autor:
Abramovich, Dan, Schober, Bernd
We show how the notion of fantastacks can be used to effectively desingularize binomial varieties defined over algebraically closed fields. In contrast to a desingularization via blow-ups in smooth centers, we drastically reduce the number of steps a
Externí odkaz:
http://arxiv.org/abs/2208.08951
Autor:
Abramovich, Dan, Quek, Ming Hao
We first introduce and study the notion of multi-weighted blow-ups, which is later used to systematically construct an explicit yet efficient algorithm for functorial logarithmic resolution in characteristic zero, in the sense of Hironaka. Specifical
Externí odkaz:
http://arxiv.org/abs/2112.06361
We introduce a variant of stable logarithmic maps, which we call punctured logarithmic maps. They allow an extension of logarithmic Gromov-Witten theory in which marked points have a negative order of tangency with boundary divisors. As a main applic
Externí odkaz:
http://arxiv.org/abs/2009.07720
In characteristic zero, we construct relative principalization of ideals for logarithmically regular morphisms of logarithmic schemes, and use it to construct logarithmically regular desingularization of morphisms. These constructions are relatively
Externí odkaz:
http://arxiv.org/abs/2003.03659
We provide a procedure for resolving, in characteristic 0, singularities of a variety $X$ embedded in a smooth variety $Y$ by repeatedly blowing up the worst singularities, in the sense of stack-theoretic weighted blowings up. No history, no exceptio
Externí odkaz:
http://arxiv.org/abs/1906.07106
Autor:
Abramovich, Dan
We discuss Hironaka's theorem on resolution of singularities in charactetistic 0 as well as more recent progress, both on simplifying and improving Hironaka's method of proof and on new results and directions on families of varieties, leading to join
Externí odkaz:
http://arxiv.org/abs/1711.09976
We prove a decomposition formula of logarithmic Gromov-Witten invariants in a degeneration setting. A one-parameter log smooth family X->B with singular fibre over b_0 \in B yields a family M(X/B,\beta) -> B of moduli stacks of stable logarithmic map
Externí odkaz:
http://arxiv.org/abs/1709.09864
Publikováno v:
Alg. Number Th. 14 (2020) 2001-2035
We show that any toroidal DM stack $X$ with finite diagonalizable inertia possesses a maximal toroidal coarsening $X_{tcs}$ such that the morphism $X\to X_{tcs}$ is logarithmically smooth. Further, we use torification results of [AT17] to construct a
Externí odkaz:
http://arxiv.org/abs/1709.03206
Given an ideal $\mathcal I$ on a variety $X$ with toroidal singularities, we produce a modification $X' \to X$, functorial for toroidal morphisms, making the ideal monomial on a toroidal stack $X'$. We do this by adapting the methods of [W{\l}o05], d
Externí odkaz:
http://arxiv.org/abs/1709.03185