Punctured Logarithmic Maps von Dan Abramovich | ISBN 9783985470860

Punctured Logarithmic Maps

von Dan Abramovich, Qile Chen, Mark Gross und Bernd Siebert
Mitwirkende
Autor / AutorinDan Abramovich
Autor / AutorinQile Chen
Autor / AutorinMark Gross
Autor / AutorinBernd Siebert
Buchcover Punctured Logarithmic Maps | Dan Abramovich | EAN 9783985470860 | ISBN 3-98547-086-3 | ISBN 978-3-98547-086-0

Punctured Logarithmic Maps

von Dan Abramovich, Qile Chen, Mark Gross und Bernd Siebert
Mitwirkende
Autor / AutorinDan Abramovich
Autor / AutorinQile Chen
Autor / AutorinMark Gross
Autor / AutorinBernd Siebert

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 application we develop a gluing formalism which reconstructs stable logarithmic maps and their virtual cycles without expansions of the target, with tropical geometry providing the underlying combinatorics.

Punctured Gromov–Witten invariants also play a pivotal role in the intrinsic construction of mirror partners by the last two authors, conjecturally relating to symplectic cohomology, and in the logarithmic gauged linear sigma model in work of Qile Chen, Felix Janda and Yongbin Ruan.