Homological mirror symmetry for log Calabi–Yau surfaces

P Hacking, A Keating - Geometry & Topology, 2023 - msp.org
Abstract Given a log Calabi–Yau surface Y with maximal boundary D and distinguished
complex structure, we explain how to construct a mirror Lefschetz fibration w: M→ ℂ, where …

Minimality and mutation-equivalence of polygons

A Kasprzyk, B Nill, T Prince - Forum of mathematics, Sigma, 2017 - cambridge.org
We introduce a concept of minimality for Fano polygons. We show that, up to mutation, there
are only finitely many Fano polygons with given singularity content, and give an algorithm to …

[HTML][HTML] Exceptional collections, and the Néron–Severi lattice for surfaces

C Vial - Advances in Mathematics, 2017 - Elsevier
We work out properties of smooth projective varieties X over a (not necessarily algebraically
closed) field k that admit collections of objects in the bounded derived category of coherent …

Cycles, derived categories, and rationality

A Auel, M Bernardara - Surveys on recent developments in …, 2017 - books.google.com
Our main goal is to give a sense of recent developments in the (stable) rationality problem
from the point of view of unramified cohomology and 0-cycles as well as derived categories …

Compact moduli spaces of surfaces and exceptional vector bundles

P Hacking, R Laza, D Oprea, P Hacking - Compactifying moduli spaces, 2016 - Springer
As shown by Kollár and Shepherd-Barron 17 the moduli space of surfaces of general type
has a natural compactification, which is analogous to the Deligne–Mumford compactification …

Exceptional collections in surface-like categories

AG Kuznetsov - Sbornik: Mathematics, 2017 - iopscience.iop.org
We provide a categorical framework for recent results of Markus Perling's on the
combinatorics of exceptional collections on numerically rational surfaces. Using it we …

On an analogue of the Markov equation for exceptional collections of length 4

LT de Volcsey, MV Bergh - arXiv preprint arXiv:1607.04246, 2016 - arxiv.org
We classify the solutions to a system of equations, introduced by Bondal, which encode
numerical constraints on full exceptional collections of length 4 on surfaces. The …

Mutations of numerically exceptional collections on surfaces

J Krah - Mathematische Zeitschrift, 2024 - Springer
A conjecture of Bondal–Polishchuk states that, in particular for the bounded derived
category of coherent sheaves on a smooth projective variety, the action of the braid group on …

Integral Chow motives of threefolds with -motives of unit type

S Gorchinskiy - arXiv preprint arXiv:1703.06977, 2017 - arxiv.org
We prove that if a smooth projective algebraic variety of dimension less or equal to three has
a unit type integral $ K $-motive, then its integral Chow motive is of Lefschetz type. As a …

[PDF][PDF] Phantoms and Exceptional Collections on Rational Surfaces

J Krah - 2024 - j-krah.github.io
This thesis is concerned with exceptional collections on smooth projective surfaces. Any
rational surface over an algebraically closed field admits a full exceptional collection. We …