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11 results on '"Shramov, C."'

1. Newton-Okounkov bodies sprouting on the valuative tree

Author

Ciliberto, C., Farnik, M., Küronya, A., Lozovanu, V., Roé, J., and Shramov, C.

Subjects
Mathematics - Algebraic Geometry
Abstract

Given a smooth projective algebraic surface X, a point O in X and a big divisor D on X, we consider the set of all Newton-Okounkov bodies of D with respect to valuations of the field of rational functions of X centred at O, or, equivalently, with respect to a flag (E,p) which is infinitely near to O, in the sense that there is a sequence of blowups mapping the smooth, irreducible rational curve E to O. The main objective of this paper is to start a systematic study of the variation of these infinitesimal Newton-Okounkov bodies as (E, p) varies, focusing on the case X = P2., Comment: 33 pages, 3 figures

Published
2016

3. The Calabi problem for smooth Fano threefolds

Author

Araujo, C, Castravet, A-M, Cheltsov, I, Fujita, K, Kaloghiros, A-S, Martinez-Garcia, J, Shramov, C, Süss, H, and Viswanathan, N

Subjects
Mathematics::Algebraic Geometry, Fano varieties, K-stability, Mathematics::Symplectic Geometry, Kähler-Einstein metrics
Abstract

To be published by CUP, LMS Lecture Notes Series 2022 Copyright © 2021 The Authors. There are 105 irreducible families of smooth Fano threefolds, which have been classified by Iskovskikh, Mori and Mukai. For each family, we determine whether its general member admits a K¨ahler–Einstein metric or not. We also find all K¨ahler–Einstein smooth Fano threefolds that have infinite automorphism groups. Engineering & Physical Sciences Research Council (EP/056689/1 Calabi conjecture for smooth Fano threefolds); Heilbronn Institute for Mathematical Research (K-stability of smooth Fano 3-folds). https://archive.mpim-bonn.mpg.de/id/eprint/4589/1/mpim-preprint_2021-31.pdf

Published
2021

5. Coble fourfold, S6-invariant quartic threefolds, and Wiman-Edge sextics

Author

Cheltsov, I., Kuznetsov, A., and Shramov, C.

Subjects
Mathematics::Algebraic Geometry
Abstract

We construct two small resolutions of singularities of the Coble fourfold (the double cover of the four-dimensional projective space branched over the Igusa quartic). We use them to show that all $S_6$-invariant three-dimensional quartics are birational to conic bundles over the quintic del Pezzo surface with the discriminant curves from the Wiman-Edge pencil. As an application, we check that $S_6$-invariant three-dimensional quartics are unirational, obtain new proofs of rationality of four special quartics among them and irrationality of the others, and describe their Weil divisor class groups as $S_6$-representations.

Published
2020

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