Boundedness of the space of stable logarithmic maps
By D. Abramovich, Qile Chen, Steffen Marcus, Jonathan Wise. 2014
61 citations recorded by the source corpus.
We prove that the moduli space of stable logarithmic maps from logarithmic curves to a fixed target logarithmic scheme is a proper algebraic stack when the target scheme is projective with fine and saturated logarithmic structure. This was previously known only with further restrictions on the logarithmic structure of the target.
View Paper: https://www.semanticscholar.org/paper/38e81f346fd5648cd294d23913e0686fca0dbfba
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
- Dhruv Ranganathan
- D. Abramovich
- Qile Chen
- Mark Gross
- Jonathan Wise
- Bernd S Siebert
- Renzo Cavalieri
- Steffen Marcus
Citations in the corpus
- Birational invariance in logarithmic Gromov–Witten theory (2013, methodology): “lgebraic spaces. Remark 2.3.4. The Artin fan of a logarithmic scheme X is representable over Log so by Lemma 2.3.1, it is an Artin fan in the sense of the first part of the definition. Remark 2.3.5. In [ACMW14] we give a more general construction of Artin fans for logarithmic schemes that are not nece”
- Skeletons and Fans of Logarithmic Structures (2015, methodology): “2X M X;y’M X;x is connected. We say X is small if it is small with respect to some point. Let N= ( X;M X). There is a canonical morphism X!A N corresponding to the morphism N!( X;M X). It is shown in [ACMW] that if Xis small this morphism is initial among all morphisms from Xto Artin fans. We theref”
- Decomposition of degenerate Gromov–Witten invariants (2017, background): “he same as discrete data = (g;A;u p i ) in Xor X 0 with the curve class A removed. Denote by M(X=B;0) the stack of basic prestable logarithmic maps in X=B, with its natural logarithmic structure. By [ACMW17] it is an algebraic stack provided with a morphism M(X=B;0) !M(X=B;0). Restricting to b 0 we ”
- A MODULI STACK OF TROPICAL CURVES (2017, background): “ffine toric variety Vσ =Speck[Sσ]by its dense torus 47 T. An Artin fan is a logarithmic algebraic stack that has a strict étale cover by a disjoint union of Artin cones. In [Uli19] and early drafts of [ACMW17] the term ‘Artin fan’ was used more inclusively for logarithmic algebraic stacks that are lo”
- Logarithmic Gromov–Witten theory with expansions (2019, background): “For a general construction, we refer the reader to [6, 10, 16, 74] and their precusor [56].”